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\par Prepared by:\tab }{Visual Information Systems Research Group
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\par \tab Princeton, NJ  08543-5300
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\par }\pard\plain \s41\fi-480\li480\nowidctlpar\widctlpar\tqr\tldot\tx8640\adjustright \caps\f4\fs20\cgrid {Figure 1.  JND Model in System Evaluation\tab 4
\par Figure 2.  Sarnoff JND Vision Algorithm Flow Chart\tab 5
\par Figure 3.  Front End Processing Overview\tab 7
\par Figure 4. Luma Processing Overview\tab 9
\par Figure 5. Chroma Processing Overview\tab 11
\par Figure 6. Luminance Contrast Sensitivity\tab 14
\par Figure 7. Luma Spatial Sensitivity\tab 15
\par Figure 8. Luma Temporal Sensitivity\tab 16
\par Figure 9. Luma Contrast Discrimination\tab 17
\par Figure 10. Disk Detection\tab 18
\par Figure 11. Checkerboard Detection\tab 19
\par Figure 12. Edge Sharpness Discrimination\tab 19
\par Figure 13. Chroma Spatial Sensitivity\tab 21
\par Figure 14.  Chroma Contrast Discrimination\tab 22
\par Figure 15. MPEG-2 Rating Predictions, 30 Fields Per Sequence.\tab 23
\par Figure 16.  MPEG-2 low bit-rate rating predictions\tab 24
\par Figure 17.  MSE predictions on low bit-rate MPEG-2 data.\tab 24
\par Figure 18. Predictions of Final Model on JPEG rating data\tab 25
\par Figure 19. RMS error predictions on JPEG rating data\tab 26
\par 
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\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab The Sarnoff JND Vision Model is a method of
 predicting the perceptual ratings that human subjects will assign to a degraded color-image sequence relative to its nondegraded counterpart.  The model takes in two image sequences and produces several difference estimates, including  a single metric of
 perceptual differences between the sequences.  These differences are quantified in units of the modeled human just-noticeable difference (JND).  A version of the model that applies only to static, achromatic images is described by Lubin (1993, 1995).

\par \tab The 
Sarnoff Vision Model can be useful in a general context (see Figure 1).  An input video sequence passes through two different channels on the way to a human observer (not shown in the figure).  One channel is uncorrupted (the reference channel), and the o
t
her distorts the image in some way (the channel under test).  The distortion, a side effect of some measure taken for economy, can occur at an encoder prior to transmission, in the transmission channel itself, or in the decoding process.  In Figure 1, the
 box called \ldblquote system under test\rdblquote 
 refers schematically to any of these alternatives.  Ordinarily, evaluation of the subjective quality of the test image relative to the reference sequence would involve the human observer and a real display device.  This evalu
ation would be facilitated by replacing the display and observer by the JND model, which compares the test and reference sequences to produce a sequence of JND maps instead of the subjective comparison.
\par 
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\par }\pard\plain \s15\qc\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\b 
\par }\pard \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright {\tab Figure 2 shows an overview of the algorithm.  The inputs are two image sequences of arbitrary length.  For each field of each input sequence, there are three data sets, labeled Y
\rquote , C}{\fs16\dn4 b}{\rquote , and C}{\fs16\dn4 r}{\rquote  at the top of Figure 2 derived, e.g., from a D1 tape.  Y, C}{\fs16\dn4 b}{, C}{\fs16\dn4 r}{
 data are then transformed to R', G', and B' electron-gun voltages that give rise to the displayed pixel values.  In the model, R', G', B' voltages undergo further processing to transform them to a luminance and two chromatic  images 
that are passed to subsequent stages. 
\par \tab The purpose of the front-end processing is to transform video input signals to light outputs, and then to transform these light outputs to psychophysically defined quantities that separately characterize luma and chroma.
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\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Toc369226404}{\*\bkmkstart _Toc369226556}{\*\bkmkstart _Ref369227520}{\*\bkmkstart _Ref369227710}{\*\bkmkstart _Toc369246577}
{\*\bkmkstart _Toc369249870}{\*\bkmkstart _Toc369436916}{\*\bkmkstart _Ref369834729}{\*\bkmkstart _Toc369915462}{\*\bkmkstart _Toc370034683}{\*\bkmkstart _Toc370042399}{\*\bkmkstart _Toc370641308}{\*\bkmkstart _Toc370641871}{\*\bkmkstart _Toc371344693}
{\*\bkmkstart _Ref371409065}{\*\bkmkstart _Toc371422859}{\*\bkmkstart _Toc371429511}{\*\bkmkstart _Toc371691774}{\*\bkmkstart _Toc371771226}{\*\bkmkstart _Toc371773578}{\*\bkmkstart _Toc371868515}{\*\bkmkstart _Toc371868711}{\*\bkmkstart _Toc371869195}
{\*\bkmkstart _Toc371950187}{\*\bkmkstart _Toc371960389}{\*\bkmkstart _Toc371996564}{\*\bkmkstart _Toc371996763}{\*\bkmkstart _Toc373146338}{\*\bkmkstart _Toc373148412}{\*\bkmkstart _Toc373151179}{\*\bkmkstart _Toc374349632}{\*\bkmkstart _Toc394995859}
Figure 2{\*\bkmkend _Ref369227520}.  Sarnoff JND Vision Algorithm Flow Chart{\*\bkmkend _Toc369226404}{\*\bkmkend _Toc369226556}{\*\bkmkend _Ref369227710}{\*\bkmkend _Toc369246577}{\*\bkmkend _Toc369249870}{\*\bkmkend _Toc369436916}
{\*\bkmkend _Ref369834729}{\*\bkmkend _Toc369915462}{\*\bkmkend _Toc370034683}{\*\bkmkend _Toc370042399}{\*\bkmkend _Toc370641308}{\*\bkmkend _Toc370641871}{\*\bkmkend _Toc371344693}{\*\bkmkend _Ref371409065}{\*\bkmkend _Toc371422859}
{\*\bkmkend _Toc371429511}{\*\bkmkend _Toc371691774}{\*\bkmkend _Toc371771226}{\*\bkmkend _Toc371773578}{\*\bkmkend _Toc371868515}{\*\bkmkend _Toc371868711}{\*\bkmkend _Toc371869195}{\*\bkmkend _Toc371950187}{\*\bkmkend _Toc371960389}
{\*\bkmkend _Toc371996564}{\*\bkmkend _Toc371996763}{\*\bkmkend _Toc373146338}{\*\bkmkend _Toc373148412}{\*\bkmkend _Toc373151179}{\*\bkmkend _Toc374349632}{\*\bkmkend _Toc394995859}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {
\par \tab A luma-processing stage accepts two images (test and reference) of luminances Y, expressed as fractions of the maximum luminance of the display.  From these inputs, the l
uma-processing stage generates a luma JND map.  This map is an image whose gray levels are proportional to the number of JNDs between the test and reference image at the corresponding pixel location.  
\par \tab Similar processing, based on the CIE L*u*v* uniform-c
olor space, occurs for each of the chroma images u* and v*.   Outputs of u* and v* processing are combined to produce the chroma JND map.  Both chroma and luma processing are influenced by inputs from the luma channel called }{\i masking}{
, which render perceived differences more or less visible depending on the structure of the luma images. 
\par \tab The chroma and luma JND maps are each available as output, together with a small number of summary measures derived from these maps.  Whereas the single JND value output is 
useful to model an observer's overall rating of the distortions in a test sequence, the JND maps give a more detailed view of the location and severity of the artifacts.
\par \tab It should be noted that two basic assumptions underlie the model presented here:
\par (a) Each pixel is square and subtends .03 degrees of viewing angle.  This number was derived from a screen height of 480 pixels, and a viewing distance of four screen-heights  (the closest viewing distance prescribed by the }{\i Rec. 500}{
  standard).  When the model
 is compared with human perception at longer viewing distances than four screen heights, the model overestimates the human's sensitivity to spatial details.  In the absence of hard constraints on viewing distance, we chose to make the model as sensitive a
s possible within the recommendations of the }{\i Rec 500}{.  (See Section 3.1.2 & 3.2)
\par }\pard \s15\sb120\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright { (b) The model applies to screen luminances of .01 to 100 ft-L (for which overall sensitivity was calibrated), but with greatest accuracy at about 20 ft-L (for which all spatio
temporal frequencies were calibrated).  It is assumed that changing luminance incurs proportional sensitivity changes at all spatiotemporal frequencies, and this assumption is less important near 20 ft-L, where more calibration took place.
\par }\pard \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright {\tab The processing shown in certain of the boxes in Figure 2 is described in more detail below, keyed to Figures 3, 4, and 5.
\par 
\par }\pard\plain \s1\sb240\sa180\keepn\pagebb\nowidctlpar\widctlpar\outlinelevel0\adjustright \b\f44\fs36\cgrid {\b0 {\*\bkmkstart B_Toc364589441}{\*\bkmkstart B_Toc365961318}{\*\bkmkstart B_Toc364582549}{\*\bkmkstart _Toc368110036}{\*\bkmkstart _Toc368112819
}{\*\bkmkstart _Toc368112866}{\*\bkmkstart _Toc368112928}{\*\bkmkstart _Toc368117520}{\*\bkmkstart _Toc368117629}{\*\bkmkstart _Toc368197219}{\*\bkmkstart _Toc368387766}{\*\bkmkstart _Toc368388264}{\*\bkmkstart _Toc368388412}{\*\bkmkstart _Toc368548942}
{\*\bkmkstart _Toc368622336}{\*\bkmkstart _Toc368649249}{\*\bkmkstart _Toc368664746}{\*\bkmkstart _Toc368752760}{\*\bkmkstart _Toc368823940}{\*\bkmkstart _Toc368828596}{\*\bkmkstart _Toc369224790}{\*\bkmkstart _Toc369249807}{\*\bkmkstart _Toc369436833}
{\*\bkmkstart _Toc369915614}{\*\bkmkstart _Toc370034601}{\*\bkmkstart _Toc370042317}{\*\bkmkstart _Toc370044428}{\*\bkmkstart _Toc370641469}{\*\bkmkstart _Toc370641808}{\*\bkmkstart _Toc371344621}{\*\bkmkstart _Toc371422794}{\*\bkmkstart _Toc371429434}
{\*\bkmkstart _Toc371432435}{\*\bkmkstart _Toc371472955}{\*\bkmkstart _Toc371691653}{\*\bkmkstart _Toc371773710}{\*\bkmkstart _Toc371868409}{\*\bkmkstart _Toc371950088}{\*\bkmkstart _Toc371960244}{\*\bkmkstart _Toc371996492}{\*\bkmkstart _Toc374349504}
{\*\bkmkstart _Toc394995841}2.\tab }{Algorithm Overview{\*\bkmkend B_Toc364589441}{\*\bkmkend B_Toc365961318}{\*\bkmkend B_Toc364582549}{\*\bkmkend _Toc368110036}{\*\bkmkend _Toc368112819}{\*\bkmkend _Toc368112866}{\*\bkmkend _Toc368112928}
{\*\bkmkend _Toc368117520}{\*\bkmkend _Toc368117629}{\*\bkmkend _Toc368197219}{\*\bkmkend _Toc368387766}{\*\bkmkend _Toc368388264}{\*\bkmkend _Toc368388412}{\*\bkmkend _Toc368548942}{\*\bkmkend _Toc368622336}{\*\bkmkend _Toc368649249}
{\*\bkmkend _Toc368664746}{\*\bkmkend _Toc368752760}{\*\bkmkend _Toc368823940}{\*\bkmkend _Toc368828596}{\*\bkmkend _Toc369224790}{\*\bkmkend _Toc369249807}{\*\bkmkend _Toc369436833}{\*\bkmkend _Toc369915614}{\*\bkmkend _Toc370034601}
{\*\bkmkend _Toc370042317}{\*\bkmkend _Toc370044428}{\*\bkmkend _Toc370641469}{\*\bkmkend _Toc370641808}{\*\bkmkend _Toc371344621}{\*\bkmkend _Toc371422794}{\*\bkmkend _Toc371429434}{\*\bkmkend _Toc371432435}{\*\bkmkend _Toc371472955}
{\*\bkmkend _Toc371691653}{\*\bkmkend _Toc371773710}{\*\bkmkend _Toc371868409}{\*\bkmkend _Toc371950088}{\*\bkmkend _Toc371960244}{\*\bkmkend _Toc371996492}{\*\bkmkend _Toc374349504}{\*\bkmkend _Toc394995841}
\par }\pard\plain \s2\sb120\sa120\keepn\nowidctlpar\widctlpar\outlinelevel1\adjustright \b\f44\fs28\cgrid {\b0 {\*\bkmkstart _Toc368117521}{\*\bkmkstart _Toc368117630}{\*\bkmkstart _Toc368197220}{\*\bkmkstart _Toc368387767}{\*\bkmkstart _Toc368388265}
{\*\bkmkstart _Toc368388413}{\*\bkmkstart _Toc368548943}{\*\bkmkstart _Toc368622337}{\*\bkmkstart _Toc368649250}{\*\bkmkstart _Toc368664747}{\*\bkmkstart _Toc368752761}{\*\bkmkstart _Toc368823941}{\*\bkmkstart _Toc368828597}{\*\bkmkstart _Toc369224791}
{\*\bkmkstart _Toc369249808}{\*\bkmkstart _Toc369436834}{\*\bkmkstart _Toc369915615}{\*\bkmkstart _Toc370034602}{\*\bkmkstart _Toc370042318}{\*\bkmkstart _Toc370044429}{\*\bkmkstart _Toc370641470}{\*\bkmkstart _Toc370641809}{\*\bkmkstart _Toc371344622}
{\*\bkmkstart _Toc371422795}{\*\bkmkstart _Toc371429435}{\*\bkmkstart _Toc371432436}{\*\bkmkstart _Toc371472956}{\*\bkmkstart _Toc371691654}{\*\bkmkstart _Toc371773711}{\*\bkmkstart _Toc371868410}{\*\bkmkstart _Toc371950089}{\*\bkmkstart _Toc371960245}
{\*\bkmkstart _Toc371996493}{\*\bkmkstart _Toc374349505}{\*\bkmkstart _Toc394995842}2.1\tab }{Front End Processing{\*\bkmkend _Toc368117521}{\*\bkmkend _Toc368117630}{\*\bkmkend _Toc368197220}{\*\bkmkend _Toc368387767}{\*\bkmkend _Toc368388265}
{\*\bkmkend _Toc368388413}{\*\bkmkend _Toc368548943}{\*\bkmkend _Toc368622337}{\*\bkmkend _Toc368649250}{\*\bkmkend _Toc368664747}{\*\bkmkend _Toc368752761}{\*\bkmkend _Toc368823941}{\*\bkmkend _Toc368828597}{\*\bkmkend _Toc369224791}
{\*\bkmkend _Toc369249808}{\*\bkmkend _Toc369436834}{\*\bkmkend _Toc369915615}{\*\bkmkend _Toc370034602}{\*\bkmkend _Toc370042318}{\*\bkmkend _Toc370044429}{\*\bkmkend _Toc370641470}{\*\bkmkend _Toc370641809}{\*\bkmkend _Toc371344622}
{\*\bkmkend _Toc371422795}{\*\bkmkend _Toc371429435}{\*\bkmkend _Toc371432436}{\*\bkmkend _Toc371472956}{\*\bkmkend _Toc371691654}{\*\bkmkend _Toc371773711}{\*\bkmkend _Toc371868410}{\*\bkmkend _Toc371950089}{\*\bkmkend _Toc371960245}
{\*\bkmkend _Toc371996493}{\*\bkmkend _Toc374349505}{\*\bkmkend _Toc394995842}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab The stack of four fields labeled Y\rquote , C}{\dn4 b}{', C}{\dn4 r}{' at the top of Figure 3 indicates a set of four consecu
tive fields from either a test or reference image sequence.  The first stage of processing transforms Y\rquote , C}{\dn4 b}{', C}{\dn4 r}{' data, to R', G', B' gun voltages.  Currently, multiple transformations are included in the software.
\par 
\par }\pard \s15\sa60\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright {\pard\plain \s15\sa60\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\pict\wmetafile8\picw18874\pich14676\picwgoal10700\pichgoal8320 \picscalex80\picscaley79 
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\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Toc369226405}{\*\bkmkstart _Toc369226557}{\*\bkmkstart _Ref369227936}{\*\bkmkstart _Ref369227956}{\*\bkmkstart _Ref369229706}
{\*\bkmkstart _Toc369246578}{\*\bkmkstart _Toc369249871}{\*\bkmkstart _Toc369436917}{\*\bkmkstart _Toc369915463}{\*\bkmkstart _Toc370034684}{\*\bkmkstart _Toc370042400}{\*\bkmkstart _Toc370641309}{\*\bkmkstart _Toc370641872}{\*\bkmkstart _Toc371344694}
{\*\bkmkstart _Toc371422860}{\*\bkmkstart _Toc371429512}{\*\bkmkstart _Toc371691775}{\*\bkmkstart _Toc371771227}{\*\bkmkstart _Toc371773579}{\*\bkmkstart _Toc371868516}{\*\bkmkstart _Toc371868712}{\*\bkmkstart _Toc371869196}{\*\bkmkstart _Toc371950188}
{\*\bkmkstart _Toc371960390}{\*\bkmkstart _Toc371996565}{\*\bkmkstart _Toc371996764}{\*\bkmkstart _Toc373146339}{\*\bkmkstart _Toc373148413}{\*\bkmkstart _Toc373151180}{\*\bkmkstart _Toc374349633}{\*\bkmkstart _Toc394995860}Figure 3
{\*\bkmkend _Ref369227936}.  Front End Processing Overview{\*\bkmkend _Toc369226405}{\*\bkmkend _Toc369226557}{\*\bkmkend _Ref369227956}{\*\bkmkend _Ref369229706}{\*\bkmkend _Toc369246578}{\*\bkmkend _Toc369249871}{\*\bkmkend _Toc369436917}
{\*\bkmkend _Toc369915463}{\*\bkmkend _Toc370034684}{\*\bkmkend _Toc370042400}{\*\bkmkend _Toc370641309}{\*\bkmkend _Toc370641872}{\*\bkmkend _Toc371344694}{\*\bkmkend _Toc371422860}{\*\bkmkend _Toc371429512}{\*\bkmkend _Toc371691775}
{\*\bkmkend _Toc371771227}{\*\bkmkend _Toc371773579}{\*\bkmkend _Toc371868516}{\*\bkmkend _Toc371868712}{\*\bkmkend _Toc371869196}{\*\bkmkend _Toc371950188}{\*\bkmkend _Toc371960390}{\*\bkmkend _Toc371996565}{\*\bkmkend _Toc371996764}
{\*\bkmkend _Toc373146339}{\*\bkmkend _Toc373148413}{\*\bkmkend _Toc373151180}{\*\bkmkend _Toc374349633}{\*\bkmkend _Toc394995860}
\par }\pard\plain \s15\qc\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\b 
\par }\pard \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright {\tab 
The second stage of processing, applied to each R', G', B' image, is a point-nonlinearity.  This stage models the transfer from R', G', B' gun voltages to model-intensities (R, G, B ) of the display (fractions of maximum lum
inance).  The nonlinearity also performs clipping at low luminances in each plane by the display. 
\par \tab Following the nonlinearity, vertical electron-beam spot spread into interline locations is modeled by replacing the interline values in fields R, G, B by in
terpolated values from above and below.  Then, the vector (R,G,B) at each pixel in the field is subjected to a linear transformation (which depends on the display phosphors) to CIE 1931 tristimulus coordinates (X, Y, Z).  The luminance component Y of this
 vector is passed to luma processing.
\par \tab To ensure (at each pixel) approximate perceptual uniformity of the color space to isoluminant color differences, we map the individual pixels into CIELUV, an international-standard uniform-color space (see Wyszecki and
 Stiles, 1982).  The chroma components u}{\up6 *}{, v}{\up6 *}{ of this space are passed to the chroma processing steps in the model.}{\fs16\up12  \chftn {\footnote \pard\plain \s27\nowidctlpar\widctlpar\adjustright \f44\fs20\cgrid {\fs13\up10 \chftn }{
 The luminance channel L}{\up6 *}{ from CIELUV is not used in luma processing, but instead is replaced by a visual nonlinearity for which the vision model has been calibrated over a range of lum
inance values.   L* is used in chroma processing, however. to create  a chroma metric that is approximately uniform and familiar to display engineers.}}}{
\par }\pard\plain \s2\sb120\sa120\keepn\nowidctlpar\widctlpar\outlinelevel1\adjustright \b\f44\fs28\cgrid {\b0 {\*\bkmkstart _Toc368117527}{\*\bkmkstart _Toc368117636}{\*\bkmkstart _Toc368197226}{\*\bkmkstart _Toc368387773}{\*\bkmkstart _Toc368388266}
{\*\bkmkstart _Toc368388414}{\*\bkmkstart _Toc368548944}{\*\bkmkstart _Toc368622338}{\*\bkmkstart _Toc368649251}{\*\bkmkstart _Toc368664748}{\*\bkmkstart _Toc368752762}{\*\bkmkstart _Toc368823942}{\*\bkmkstart _Toc368828598}{\*\bkmkstart _Toc369224792}
{\*\bkmkstart _Toc369249809}{\*\bkmkstart _Toc369436835}{\*\bkmkstart _Toc369915616}{\*\bkmkstart _Toc370034603}{\*\bkmkstart _Toc370042319}{\*\bkmkstart _Toc370044430}{\*\bkmkstart _Toc370641471}{\*\bkmkstart _Toc370641810}{\*\bkmkstart _Toc371344623}
{\*\bkmkstart _Toc371422796}{\*\bkmkstart _Toc371429436}{\*\bkmkstart _Toc371432437}{\*\bkmkstart _Toc371472957}{\*\bkmkstart _Toc371691655}{\*\bkmkstart _Toc371773712}{\*\bkmkstart _Toc371868411}{\*\bkmkstart _Toc371950090}{\*\bkmkstart _Toc371960246}
{\*\bkmkstart _Toc371996494}{\*\bkmkstart _Ref373144321}{\*\bkmkstart _Toc374349506}{\*\bkmkstart _Toc394995843}2.2\tab }{Luma Processing{\*\bkmkend _Toc368117527}{\*\bkmkend _Toc368117636}{\*\bkmkend _Toc368197226}{\*\bkmkend _Toc368387773}
{\*\bkmkend _Toc368388266}{\*\bkmkend _Toc368388414}{\*\bkmkend _Toc368548944}{\*\bkmkend _Toc368622338}{\*\bkmkend _Toc368649251}{\*\bkmkend _Toc368664748}{\*\bkmkend _Toc368752762}{\*\bkmkend _Toc368823942}{\*\bkmkend _Toc368828598}
{\*\bkmkend _Toc369224792}{\*\bkmkend _Toc369249809}{\*\bkmkend _Toc369436835}{\*\bkmkend _Toc369915616}{\*\bkmkend _Toc370034603}{\*\bkmkend _Toc370042319}{\*\bkmkend _Toc370044430}{\*\bkmkend _Toc370641471}{\*\bkmkend _Toc370641810}
{\*\bkmkend _Toc371344623}{\*\bkmkend _Toc371422796}{\*\bkmkend _Toc371429436}{\*\bkmkend _Toc371432437}{\*\bkmkend _Toc371472957}{\*\bkmkend _Toc371691655}{\*\bkmkend _Toc371773712}{\*\bkmkend _Toc371868411}{\*\bkmkend _Toc371950090}
{\*\bkmkend _Toc371960246}{\*\bkmkend _Toc371996494}{\*\bkmkend _Ref373144321}{\*\bkmkend _Toc374349506}{\*\bkmkend _Toc394995843}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab As shown in Figure 4, each luma value is first subjected to a compressive nonlinearity.  Then, each luma field is fil
tered and down-sampled in a four-level Gaussian pyramid (Burt and Adelson, 1983), in order to model the psychophysically and physiologically observed decomposition of incoming visual signals into different spatial-frequency bands.  After this decompositio
n, the bulk of subsequent processing by the model consists of similar operations (e.g., oriented filtering) performed at each pyramid level.  
\par \tab After this pyramid-making process, the lowest-resolution pyramid image is subjected to temporal filtering and con
trast computation, and the other three levels are subjected to spatial filtering and contrast computation.  In each case the contrast is a local difference of pixel values divided by a local sum, appropriately scaled.  In the initial formulation of the mo
del, this established the definition of 1 JND, which was passed on to subsequent stages of the model.}{\fs16\up12 \chftn {\footnote \pard\plain \s27\nowidctlpar\widctlpar\adjustright \f44\fs20\cgrid {\fs13\up10 \chftn }{
 The association of a constant contrast with 1 JND is an implementation of what is known as Weber's law for vision.}}}{
  (Calibration iteratively revises the 1-JND interpretation at intermediate model stages.  This is discussed in Section 3.1.)  The absolute value of the co
ntrast response is passed to the following stage, and the algebraic sign is preserved for reattachment just prior to image comparison (JND map computation).  
\par 
\par }\pard \s15\sa60\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright {\pard\plain \s15\sa60\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\pict\wmetafile8\picw22684\pich16228\picwgoal12860\pichgoal9200 \picscalex67\picscaley67 
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\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Toc369226406}{\*\bkmkstart _Toc369226558}{\*\bkmkstart _Ref369228205}{\*\bkmkstart _Ref369228249}{\*\bkmkstart _Toc369246579}
{\*\bkmkstart _Toc369249872}{\*\bkmkstart _Toc369436918}{\*\bkmkstart _Ref369834826}{\*\bkmkstart _Toc369915464}{\*\bkmkstart _Toc370034685}{\*\bkmkstart _Toc370042401}{\*\bkmkstart _Toc370641310}{\*\bkmkstart _Toc370641873}{\*\bkmkstart _Toc371344695}
{\*\bkmkstart _Toc371422861}{\*\bkmkstart _Toc371429513}{\*\bkmkstart _Toc371691776}{\*\bkmkstart _Toc371771228}{\*\bkmkstart _Toc371773580}{\*\bkmkstart _Toc371868517}{\*\bkmkstart _Toc371868713}{\*\bkmkstart _Toc371869197}{\*\bkmkstart _Toc371950189}
{\*\bkmkstart _Toc371960391}{\*\bkmkstart _Toc371996566}{\*\bkmkstart _Toc371996765}{\*\bkmkstart _Toc373146340}{\*\bkmkstart _Toc373148414}{\*\bkmkstart _Toc373151181}{\*\bkmkstart _Toc374349634}{\*\bkmkstart _Toc394995861}Figure 4
{\*\bkmkend _Ref369228205}. Luma Processing Overview{\*\bkmkend _Toc369226406}{\*\bkmkend _Toc369226558}{\*\bkmkend _Ref369228249}{\*\bkmkend _Toc369246579}{\*\bkmkend _Toc369249872}{\*\bkmkend _Toc369436918}{\*\bkmkend _Ref369834826}
{\*\bkmkend _Toc369915464}{\*\bkmkend _Toc370034685}{\*\bkmkend _Toc370042401}{\*\bkmkend _Toc370641310}{\*\bkmkend _Toc370641873}{\*\bkmkend _Toc371344695}{\*\bkmkend _Toc371422861}{\*\bkmkend _Toc371429513}{\*\bkmkend _Toc371691776}
{\*\bkmkend _Toc371771228}{\*\bkmkend _Toc371773580}{\*\bkmkend _Toc371868517}{\*\bkmkend _Toc371868713}{\*\bkmkend _Toc371869197}{\*\bkmkend _Toc371950189}{\*\bkmkend _Toc371960391}{\*\bkmkend _Toc371996566}{\*\bkmkend _Toc371996765}
{\*\bkmkend _Toc373146340}{\*\bkmkend _Toc373148414}{\*\bkmkend _Toc373151181}{\*\bkmkend _Toc374349634}{\*\bkmkend _Toc394995861}
\par }\pard\plain \s15\qc\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\b 
\par }\pard \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright {\tab The next stage (contrast maskin
g) is a gain-setting operation in which each oriented contrast response is divided by a function of all the contrast responses.  This combined attenuation of each response by other local responses is included to model visual "masking" effects such as the 
d
ecrease in sensitivity to distortions in "busy" image areas (Nachmias and Sansbury, 1974).  At this stage in the model, temporal structure (flicker) is made to mask spatial differences, and spatial structure is also made to mask temporal differences.   Lu
ma masking is also applied on the chroma side, as discussed below.
\par \tab The masked contrast responses (together with the contrast signs) are used to produce the Luma JND map.  This is done by:
\par }\pard \s15\fi-360\li720\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright {\f3 \u8721\'11\tab }{separating each image into positive and negative components (half-wave rectification)
\par }{\f3 \u8721\'11\tab }{performing local pooling (averaging and downsampling, to model the local spatial summation observed in psychophysical experiments)
\par }{\f3 \u8721\'11\tab }{evaluating the absolute image differences channel by channel
\par }{\f3 \u8721\'11\tab }{up-sampling to the same resolution (which will be half the resolution of the original image due to the pooling stage). 
\par }{\f3 \u8721\'11\tab }{evaluating the sum over all channels, and also (in parallel) the maximum in all channels  
\par }{\f3 \u8721\'11\tab }{evaluating a linear combination of the channel-sum and the channel-maximum (an approximation to a Minkowski norm that was necessitated by limits on integer implementation)
\par }\pard\plain \s2\sb120\sa120\keepn\nowidctlpar\widctlpar\outlinelevel1\adjustright \b\f44\fs28\cgrid {\b0 {\*\bkmkstart _Toc368117534}{\*\bkmkstart _Toc368117643}{\*\bkmkstart _Toc368197233}{\*\bkmkstart _Toc368387780}{\*\bkmkstart _Toc368388267}
{\*\bkmkstart _Toc368388415}{\*\bkmkstart _Toc368548945}{\*\bkmkstart _Toc368622339}{\*\bkmkstart _Toc368649252}{\*\bkmkstart _Toc368664749}{\*\bkmkstart _Toc368752763}{\*\bkmkstart _Toc368823943}{\*\bkmkstart _Toc368828599}{\*\bkmkstart _Toc369224793}
{\*\bkmkstart _Toc369249810}{\*\bkmkstart _Toc369436836}{\*\bkmkstart _Toc369915617}{\*\bkmkstart _Toc370034604}{\*\bkmkstart _Toc370042320}{\*\bkmkstart _Toc370044431}{\*\bkmkstart _Toc370641472}{\*\bkmkstart _Toc370641811}{\*\bkmkstart _Toc371344624}
{\*\bkmkstart _Ref371391604}{\*\bkmkstart _Toc371422797}{\*\bkmkstart _Toc371429437}{\*\bkmkstart _Toc371432438}{\*\bkmkstart _Toc371472958}{\*\bkmkstart _Toc371691656}{\*\bkmkstart _Toc371773713}{\*\bkmkstart _Toc371868412}{\*\bkmkstart _Toc371950091}
{\*\bkmkstart _Toc371960247}{\*\bkmkstart _Toc371996495}{\*\bkmkstart _Toc374349507}{\*\bkmkstart _Toc394995844}2.3\tab }{Chroma Processing{\*\bkmkend _Toc368117534}{\*\bkmkend _Toc368117643}{\*\bkmkend _Toc368197233}{\*\bkmkend _Toc368387780}
{\*\bkmkend _Toc368388267}{\*\bkmkend _Toc368388415}{\*\bkmkend _Toc368548945}{\*\bkmkend _Toc368622339}{\*\bkmkend _Toc368649252}{\*\bkmkend _Toc368664749}{\*\bkmkend _Toc368752763}{\*\bkmkend _Toc368823943}{\*\bkmkend _Toc368828599}
{\*\bkmkend _Toc369224793}{\*\bkmkend _Toc369249810}{\*\bkmkend _Toc369436836}{\*\bkmkend _Toc369915617}{\*\bkmkend _Toc370034604}{\*\bkmkend _Toc370042320}{\*\bkmkend _Toc370044431}{\*\bkmkend _Toc370641472}{\*\bkmkend _Toc370641811}
{\*\bkmkend _Toc371344624}{\*\bkmkend _Ref371391604}{\*\bkmkend _Toc371422797}{\*\bkmkend _Toc371429437}{\*\bkmkend _Toc371432438}{\*\bkmkend _Toc371472958}{\*\bkmkend _Toc371691656}{\*\bkmkend _Toc371773713}{\*\bkmkend _Toc371868412}
{\*\bkmkend _Toc371950091}{\*\bkmkend _Toc371960247}{\*\bkmkend _Toc371996495}{\*\bkmkend _Toc374349507}{\*\bkmkend _Toc394995844}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab Chroma processing parallels luma processing in several ways.  Intra-imag
e differences of chroma (u* and v*) of the CIELUV space are used to define the detection thresholds for the chroma model, in analogy to the way the Michelson contrast (and Weber's law) is used to define the detection threshold in the luminance model. Also
, in analogy with the luminance model, the chromatic "contrasts" defined by u}{\up6 *}{ and v}{\up6 *}{
 differences are subjected to a masking step.  A transducer nonlinearity makes the discrimination of a contrast increment between one image and another depend on the contrast response that is common to both images.
\par \tab Figure 5 shows that, as in luma processing, each chroma component u*, v* is subjected to pyramid decomposition.  However, whereas luma processing needs only four pyramid levels, chroma processing is given seven l
evels.  This captures the empirical fact that chromatic channels are sensitive to far lower spatial frequencies than luma channels (Mullen, 1985).  Also, it takes into account the intuitive fact that color differences can be observed in large, uniform reg
ions.
\par \tab To reflect the inherent insensitivity of the chroma channels to flicker, temporal processing is accomplished by averaging over four image fields. 
\par \tab  Then, spatial filtering by a Laplacian kernel is performed in u* and v* .  This operation produces a 
color difference in u*, v*, which (by definition of the uniform color space) is metrically connected to just-noticeable color differences. A value of 1 at this stage is taken to mean a single JND has been achieved, in analogy to the role of Weber's-law-ba
sed contrast in the luma channel. (As in the case of luma, the 1-JND chroma unit must undergo reinterpretation during calibration.)
\par 
\par }\pard \s15\sa60\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright {\pard\plain \s15\sa60\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\pict\wmetafile8\picw24765\pich16334\picwgoal14040\pichgoal9260 \picscalex61\picscaley60 
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ffff0100000000000000040000002701ffff030000000000}}}{
\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Toc369226407}{\*\bkmkstart _Toc369226559}{\*\bkmkstart _Ref369229031}{\*\bkmkstart _Toc369246580}{\*\bkmkstart _Toc369249873}
{\*\bkmkstart _Toc369436919}{\*\bkmkstart _Toc369915465}{\*\bkmkstart _Toc370034686}{\*\bkmkstart _Toc370042402}{\*\bkmkstart _Toc370641311}{\*\bkmkstart _Toc370641874}{\*\bkmkstart _Toc371344696}{\*\bkmkstart _Toc371422862}{\*\bkmkstart _Toc371429514}
{\*\bkmkstart _Toc371691777}{\*\bkmkstart _Toc371771229}{\*\bkmkstart _Toc371773581}{\*\bkmkstart _Toc371868518}{\*\bkmkstart _Toc371868714}{\*\bkmkstart _Toc371869198}{\*\bkmkstart _Toc371950190}{\*\bkmkstart _Toc371960392}{\*\bkmkstart _Toc371996567}
{\*\bkmkstart _Toc371996766}{\*\bkmkstart _Toc373146341}{\*\bkmkstart _Toc373148415}{\*\bkmkstart _Toc373151182}{\*\bkmkstart _Toc374349635}{\*\bkmkstart _Toc394995862}Figure 5{\*\bkmkend _Ref369229031}. Chroma Processing Overview{\*\bkmkend _Toc369226407
}{\*\bkmkend _Toc369226559}{\*\bkmkend _Toc369246580}{\*\bkmkend _Toc369249873}{\*\bkmkend _Toc369436919}{\*\bkmkend _Toc369915465}{\*\bkmkend _Toc370034686}{\*\bkmkend _Toc370042402}{\*\bkmkend _Toc370641311}{\*\bkmkend _Toc370641874}
{\*\bkmkend _Toc371344696}{\*\bkmkend _Toc371422862}{\*\bkmkend _Toc371429514}{\*\bkmkend _Toc371691777}{\*\bkmkend _Toc371771229}{\*\bkmkend _Toc371773581}{\*\bkmkend _Toc371868518}{\*\bkmkend _Toc371868714}{\*\bkmkend _Toc371869198}
{\*\bkmkend _Toc371950190}{\*\bkmkend _Toc371960392}{\*\bkmkend _Toc371996567}{\*\bkmkend _Toc371996766}{\*\bkmkend _Toc373146341}{\*\bkmkend _Toc373148415}{\*\bkmkend _Toc373151182}{\*\bkmkend _Toc374349635}{\*\bkmkend _Toc394995862}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {
\par \tab This color difference value is weighted, absolute-valued,
 and passed (with the contrast algebraic sign) to the contrast-masking stage.  The masking stage performs the same function as it did in the luma model.  It is somewhat simpler, since it receives input only from the luma channels and from the chroma chann
el whose difference is being evaluated.  Finally, the masked contrast responses are processed exactly as in the luma model (see last paragraph of Section 2.2).
\par }\pard\plain \s2\sb120\sa120\keepn\nowidctlpar\widctlpar\outlinelevel1\adjustright \b\f44\fs28\cgrid {\b0 {\*\bkmkstart _Toc368117542}{\*\bkmkstart _Toc368117651}{\*\bkmkstart _Toc368197241}{\*\bkmkstart _Toc368387788}{\*\bkmkstart _Toc368388268}
{\*\bkmkstart _Toc368388416}{\*\bkmkstart _Toc368548946}{\*\bkmkstart _Toc368622340}{\*\bkmkstart _Toc368649253}{\*\bkmkstart _Toc368664750}{\*\bkmkstart _Toc368752764}{\*\bkmkstart _Toc368823944}{\*\bkmkstart _Toc368828600}{\*\bkmkstart _Toc369224794}
{\*\bkmkstart _Toc369249811}{\*\bkmkstart _Toc369436837}{\*\bkmkstart _Toc369915618}{\*\bkmkstart _Toc370034605}{\*\bkmkstart _Toc370042321}{\*\bkmkstart _Toc370044432}{\*\bkmkstart _Toc370641473}{\*\bkmkstart _Toc370641812}{\*\bkmkstart _Toc371344625}
{\*\bkmkstart _Toc371422798}{\*\bkmkstart _Toc371429438}{\*\bkmkstart _Toc371432439}{\*\bkmkstart _Toc371472959}{\*\bkmkstart _Toc371691657}{\*\bkmkstart _Toc371773714}{\*\bkmkstart _Toc371868413}{\*\bkmkstart _Toc371950092}{\*\bkmkstart _Toc371960248}
{\*\bkmkstart _Toc371996496}{\*\bkmkstart _Toc374349508}{\*\bkmkstart _Toc394995845}2.4\tab }{JND Output Summaries{\*\bkmkend _Toc368117542}{\*\bkmkend _Toc368117651}{\*\bkmkend _Toc368197241}{\*\bkmkend _Toc368387788}{\*\bkmkend _Toc368388268}
{\*\bkmkend _Toc368388416}{\*\bkmkend _Toc368548946}{\*\bkmkend _Toc368622340}{\*\bkmkend _Toc368649253}{\*\bkmkend _Toc368664750}{\*\bkmkend _Toc368752764}{\*\bkmkend _Toc368823944}{\*\bkmkend _Toc368828600}{\*\bkmkend _Toc369224794}
{\*\bkmkend _Toc369249811}{\*\bkmkend _Toc369436837}{\*\bkmkend _Toc369915618}{\*\bkmkend _Toc370034605}{\*\bkmkend _Toc370042321}{\*\bkmkend _Toc370044432}{\*\bkmkend _Toc370641473}{\*\bkmkend _Toc370641812}{\*\bkmkend _Toc371344625}
{\*\bkmkend _Toc371422798}{\*\bkmkend _Toc371429438}{\*\bkmkend _Toc371432439}{\*\bkmkend _Toc371472959}{\*\bkmkend _Toc371691657}{\*\bkmkend _Toc371773714}{\*\bkmkend _Toc371868413}{\*\bkmkend _Toc371950092}{\*\bkmkend _Toc371960248}
{\*\bkmkend _Toc371996496}{\*\bkmkend _Toc374349508}{\*\bkmkend _Toc394995845}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab For each field in the video-sequence comparison, the luma and chroma JN
D maps are first reduced to single-number summaries, namely luma and chroma Picture Quality Ratings (PQRs).   In each case, the reduction from map to number  is done by histogramming the JND values for all pixels above a threshold, and then adopting the 9
0
-percent value as the PQR value.  Then, the luma and chroma PQR numbers are combined, again via a linear combination of a sum and a maximum, to produce the PQR estimate for the field being processed.  A single performance measure for many fields of a vide
o sequence is determined from the single-field PQRs by evaluating the 90th percentile of either: 
\par }\pard \s15\fi-360\li720\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright {\f3 \u8721\'11\tab }{the actual histogram of single-field PQR values
\par }\pard \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright {or, for short sequences,
\par }\pard \s15\fi-360\li720\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright {\f3 \u8721\'11\tab }{a "faux histogram" fit to the actual histogram.
\par }\pard\plain \s1\sb240\sa180\keepn\pagebb\nowidctlpar\widctlpar\outlinelevel0\adjustright \b\f44\fs36\cgrid {\b0 {\*\bkmkstart B_Toc364589443}{\*\bkmkstart B_Toc365961320}{\*\bkmkstart B_Toc364582551}{\*\bkmkstart _Toc368110038}{\*\bkmkstart _Toc368112821
}{\*\bkmkstart _Toc368112870}{\*\bkmkstart _Toc368112930}{\*\bkmkstart _Toc368117544}{\*\bkmkstart _Toc368117653}{\*\bkmkstart _Toc368197243}{\*\bkmkstart _Toc368387812}{\*\bkmkstart _Toc368388291}{\*\bkmkstart _Toc368388439}{\*\bkmkstart _Toc368548967}
{\*\bkmkstart _Toc368622361}{\*\bkmkstart _Toc368649274}{\*\bkmkstart _Toc368664771}{\*\bkmkstart _Toc368752785}{\*\bkmkstart _Toc371422821}{\*\bkmkstart _Toc371429461}{\*\bkmkstart _Toc371432464}{\*\bkmkstart _Toc371472989}{\*\bkmkstart _Toc371691681}
{\*\bkmkstart _Toc371773738}{\*\bkmkstart _Toc371868437}{\*\bkmkstart _Toc371950116}{\*\bkmkstart _Toc371960272}{\*\bkmkstart _Toc371996520}{\*\bkmkstart _Ref374345906}{\*\bkmkstart _Ref374346023}{\*\bkmkstart _Toc374349532}{\*\bkmkstart _Ref378138292}
{\*\bkmkstart _Ref378414457}{\*\bkmkstart _Toc394995846}3.\tab }{Luma Calibration and Prediction{\*\bkmkend _Toc371422821}{\*\bkmkend _Toc371429461}{\*\bkmkend _Toc371432464}{\*\bkmkend _Toc371472989}{\*\bkmkend _Toc371691681}{\*\bkmkend _Toc371773738}
{\*\bkmkend _Toc371868437}{\*\bkmkend _Toc371950116}{\*\bkmkend _Toc371960272}{\*\bkmkend _Toc371996520}{\*\bkmkend _Ref374345906}{\*\bkmkend _Ref374346023}{\*\bkmkend _Toc374349532}{\*\bkmkend _Ref378138292}{\*\bkmkend _Ref378414457}
{\*\bkmkend _Toc394995846}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab 
Psychophysical data were used for two purposes, to calibrate the luma model (i.e., to determine values for certain model parameters), and to confirm the predictive value of the luma model once it was calibrated.  In all cases, the stimuli were injected i
nto the model as Y-value images immediately prior to the luma processing.
\par }\pard\plain \s2\sb120\sa120\keepn\nowidctlpar\widctlpar\outlinelevel1\adjustright \b\f44\fs28\cgrid {\b0 {\*\bkmkstart _Toc368828622}{\*\bkmkstart _Toc369224816}{\*\bkmkstart _Toc369249833}{\*\bkmkstart _Toc369436859}{\*\bkmkstart _Toc369915642}
{\*\bkmkstart _Toc370034629}{\*\bkmkstart _Toc370042351}{\*\bkmkstart _Toc370044456}{\*\bkmkstart _Toc370641497}{\*\bkmkstart _Toc370641836}{\*\bkmkstart _Toc371344649}{\*\bkmkstart _Ref371406772}{\*\bkmkstart _Toc371422822}{\*\bkmkstart _Toc371429462}
{\*\bkmkstart _Toc371432500}{\*\bkmkstart _Toc371473033}{\*\bkmkstart _Toc371691683}{\*\bkmkstart _Toc371773754}{\*\bkmkstart _Toc371868438}{\*\bkmkstart _Toc371950117}{\*\bkmkstart _Toc371960273}{\*\bkmkstart _Toc371996521}{\*\bkmkstart _Toc374349533}
{\*\bkmkstart _Toc394995847}3.1\tab }{Calibration{\*\bkmkend _Toc368828622}{\*\bkmkend _Toc369224816}{\*\bkmkend _Toc369249833}{\*\bkmkend _Toc369436859}{\*\bkmkend _Toc369915642}{\*\bkmkend _Toc370034629}{\*\bkmkend _Toc370042351}
{\*\bkmkend _Toc370044456}{\*\bkmkend _Toc370641497}{\*\bkmkend _Toc370641836}{\*\bkmkend _Toc371344649}{\*\bkmkend _Ref371406772}{\*\bkmkend _Toc371422822}{\*\bkmkend _Toc371429462}{\*\bkmkend _Toc371432500}{\*\bkmkend _Toc371473033}
{\*\bkmkend _Toc371691683}{\*\bkmkend _Toc371773754}{\*\bkmkend _Toc371868438}{\*\bkmkend _Toc371950117}{\*\bkmkend _Toc371960273}{\*\bkmkend _Toc371996521}{\*\bkmkend _Toc374349533}{\*\bkmkend _Toc394995847}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab The luma model was calibrated iteratively, using three sets of data.   One data set was used to adjust the constants in the luma-compression step.  The second data s
et was used to adjust the filtering and contrast of the mode (see Figure 4).  The third set was used to adjust the masking-stage constants.
\par \tab The details of the luma-compression adjustments are described in the subsections below.
\par }\pard\plain \s3\sb120\sa120\keepn\nowidctlpar\widctlpar\outlinelevel2\adjustright \b\f44\cgrid {\b0 {\*\bkmkstart B_Toc374349534_1}{\*\bkmkstart B_Toc390058187_2}{\*\bkmkstart B_Toc371996522_3}{\*\bkmkstart B_Toc371960274_4}{\*\bkmkstart B_Toc371950118_5
}{\*\bkmkstart B_Toc371868439_6}{\*\bkmkstart B_Toc371773755_7}{\*\bkmkstart B_Toc371691684_8}{\*\bkmkstart B_Toc371473034_9}{\*\bkmkstart B_Toc371432501_10}{\*\bkmkstart B_Toc371429463_11}{\*\bkmkstart B_Toc371422823_12}{\*\bkmkstart B_Toc371344650_13}
{\*\bkmkstart B_Toc370641837_14}{\*\bkmkstart B_Toc370641498_15}{\*\bkmkstart B_Toc370044457_16}{\*\bkmkstart B_Toc370042352_17}{\*\bkmkstart B_Toc370034630_18}{\*\bkmkstart _Toc394995848}3.1.1\tab }{Adjustment of luma-compression 
{\*\bkmkend B_Toc374349534_1}{\*\bkmkend B_Toc390058187_2}{\*\bkmkend B_Toc371996522_3}{\*\bkmkend B_Toc371960274_4}{\*\bkmkend B_Toc371950118_5}{\*\bkmkend B_Toc371868439_6}{\*\bkmkend B_Toc371773755_7}{\*\bkmkend B_Toc371691684_8}
{\*\bkmkend B_Toc371473034_9}{\*\bkmkend B_Toc371432501_10}{\*\bkmkend B_Toc371429463_11}{\*\bkmkend B_Toc371422823_12}{\*\bkmkend B_Toc371344650_13}{\*\bkmkend B_Toc370641837_14}{\*\bkmkend B_Toc370641498_15}{\*\bkmkend B_Toc370044457_16}
{\*\bkmkend B_Toc370042352_17}constants{\*\bkmkend B_Toc370034630_18}{\*\bkmkend _Toc394995848}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab 
The model predictions for sine-wave contrast sensitivity at various luminances were matched to contrast-sensitivity data for 8-cycles/deg sine waves presented by Van Nes et al. (1967) and reproduced by R. J. Farrell and J. M. Booth, }{\i De
sign Handbook for Imagery Interpretation Equipment}{
   (Boeing Aerospace Co., 1975, Report D180-19063-1) Fig. 3.2-33.  To generate points on the model-based curve, a low-amplitude spatial sine wave at 8-cycles/deg was presented as a test image to the model, 
and the contrast threshold for 1 JND output was assessed.  In each case the reference image implicitly had a uniform field with the same average luminance as the test field. 
\par \tab It should be noted that the Van Nes data expressed the light level in trolands of retinal illumination, not in external luminance (cd/m}{\up6 2}{).  However, because Van Nes et al. used an artificial 2-mm pupil, the conversion from trolands to cd/m}{
\up6 2}{ became a simple division by }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\dn4\cgrid {\object\objemb\rsltmerge\objw200\objh180\objcropl-10\objcropr-10{\*\objclass Equation.3}{\*\objdata 01050000020000000b000000
4571756174696f6e2e330000000000000000000c00000002000101000a01028470000001050000050000000d0000004d45544146494c455049435400d400000041ffffffd00000000800d400bf000000
010009000003640000000100100000000000050000000b0200000000050000000c0209000a000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff0000000000009001
020000020000005053796d626f6c0000040000002d01000007000000210501007000070001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn4 {\pict\wmetafile8\picw212\pich191\picwgoal200\pichgoal180 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c0209000a000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900102
0000020000005053796d626f6c0000040000002d01000007000000210501007000070001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}}}}}{. 
\par \tab The fit of spatial contrast sensitivity to data (see Figure 6 for final fit) was used to adjust two luma-compression constants.  The solid line in Figure 6 represents the sensitivity predictions of the model.  
\par \tab It should be noted that the domain of the model fit was chosen to include the total range of luminances expected from the model display, or .01 to 100 ft-L.  (The conversion from ft-L to cd/m}{\up6 2}{ involves multiplying by 3.4). 
\par 
\par }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\pict\wmetafile8\picw13547\pich7620\picwgoal7680\pichgoal4320 \piccropl-10\piccropr-10 
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0f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000800000021050400302e3031700078fb0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000800000021050300302e3100c0fea8fb0b00000026060f000c00ffffff
ff01000000000000000b00000026060f000c00ffffffff00000000000000000700000021050100310008fdf0fb0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000800000021050400302e3031980210fc0b00000026060f000c00ffffffff0100000000000000
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ff00000000000000000500000009020000000010000000fb02b8ff0000000000009001000000000000002047656e6576610000040000002d01050004000000f00103000c00000021050b00764e2026204220646174610050fd70030b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff
000000000000000009000000fa02060010000000008011002200040000002d01030004000000f001000005000000140298fd940205000000130298fd5c030b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000b000000210509004a4e44204d6f64656c00c0fd70
030b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}}}{
\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Ref392136084}{\*\bkmkstart _Toc394995863}Figure 6{\*\bkmkend _Ref392136084}. Luminance Contrast Sensitivity{\*\bkmkend _Toc394995863}
\par }\pard\plain \s3\sb120\sa120\keepn\nowidctlpar\widctlpar\outlinelevel2\adjustright \b\f44\cgrid {\b0 {\*\bkmkstart _Toc370034630}{\*\bkmkstart _Toc370042352}{\*\bkmkstart _Toc370044457}{\*\bkmkstart _Toc370641498}{\*\bkmkstart _Toc370641837}
{\*\bkmkstart _Toc371344650}{\*\bkmkstart _Toc371422823}{\*\bkmkstart _Toc371429463}{\*\bkmkstart _Toc371432501}{\*\bkmkstart _Toc371473034}{\*\bkmkstart _Toc371691684}{\*\bkmkstart _Toc371773755}{\*\bkmkstart _Toc371868439}{\*\bkmkstart _Toc371950118}
{\*\bkmkstart _Toc371960274}{\*\bkmkstart _Toc371996522}{\*\bkmkstart _Toc374349534}{\*\bkmkstart _Toc394995849}3.1.2\tab }{Adjustment of contrast-normalization constants{\*\bkmkend _Toc370034630}{\*\bkmkend _Toc370042352}{\*\bkmkend _Toc370044457}
{\*\bkmkend _Toc370641498}{\*\bkmkend _Toc370641837}{\*\bkmkend _Toc371344650}{\*\bkmkend _Toc371422823}{\*\bkmkend _Toc371429463}{\*\bkmkend _Toc371432501}{\*\bkmkend _Toc371473034}{\*\bkmkend _Toc371691684}{\*\bkmkend _Toc371773755}
{\*\bkmkend _Toc371868439}{\*\bkmkend _Toc371950118}{\*\bkmkend _Toc371960274}{\*\bkmkend _Toc371996522}{\*\bkmkend _Toc374349534}{\*\bkmkend _Toc394995849}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab 
The model predictions for spatial and temporal contrast sensitivities prior to masking were matched to contrast-sensitivity data for sine waves presented by Koenderink and Van Doorn (1979). To generate points on the model-based cur
ve, a low-amplitude sine wave was presented as a test image to the model (either in space or in time), and the contrast threshold for 1 JND output was assessed.  In each case the reference image implicitly had a uniform field with the same average luminan
ce as the test field.
\par \tab The fit of spatial contrast sensitivity to data (see Figure 7 for final fit) was used to adjust the contrast-pyramid sensitivity parameters.  The dashed lines in Figure 7 represent the sensitivities of the separate pyramid channels th
at comprise the total sensitivity (solid line).  It should be noted that the spatial model fit in Figure 7 was not extended beyond 15 cycles/deg, consistent with the viewing-distance constraint discussed in the System Overview:  a viewing distance of four
 
screen-heights.  Similar adjustment of these constants could be performed to accommodate slightly different viewing distances; much greater viewing distances might require lower-resolution pyramid levels, and these could be easily incorporated at low comp
utational expense. 
\par \tab }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\pict\wmetafile8\picw12347\pich10442\picwgoal7000\pichgoal5920 \piccropl-10\piccropr-10 
010009000003dd1100000600350000000000050000000b0248fb98fa050000000c024009f00a0400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff00000000000000000b00000026060f000c00ffffffff000000
00000000000b00000026060f000c00ffffffff000000000000000009000000fa02060008000000000000002200040000002d010000050000001402ccfb54fc0500000013023c0354fc0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0000000000000000050000001402ccfb3cfc
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000000000000000b00000026060f000c00ffffffff00000000000000000a000000250303003002b0fe2802b0fe2002b8fe0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000009000000fa0206000b000000000000002200040000002d01000004000000f0010100
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\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Ref371770555}{\*\bkmkstart _Toc371771238}{\*\bkmkstart _Toc371773588}{\*\bkmkstart _Toc371868560}{\*\bkmkstart _Toc371868740}
{\*\bkmkstart _Toc371869204}{\*\bkmkstart _Toc371950199}{\*\bkmkstart _Toc371960399}{\*\bkmkstart _Toc371996772}{\*\bkmkstart _Toc373146348}{\*\bkmkstart _Toc373148423}{\*\bkmkstart _Toc373151189}{\*\bkmkstart _Toc374349647}{\*\bkmkstart _Toc394995864}
Figure 7{\*\bkmkend _Ref371770555}. Luma Spatial Sensitivity{\*\bkmkend _Toc371771238}{\*\bkmkend _Toc371773588}{\*\bkmkend _Toc371868560}{\*\bkmkend _Toc371868740}{\*\bkmkend _Toc371869204}{\*\bkmkend _Toc371950199}{\*\bkmkend _Toc371960399}
{\*\bkmkend _Toc371996772}{\*\bkmkend _Toc373146348}{\*\bkmkend _Toc373148423}{\*\bkmkend _Toc373151189}{\*\bkmkend _Toc374349647}{\*\bkmkend _Toc394995864}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab 
The fit of temporal contrast-sensitivity to data (see Figure 8 for final fits) was used to adjust the temporal filter-tap parameters, as well as the contrast-pyramid sensit
ivity parameter. The method used to fit these parameters is analogous to the spatial-contrast calibration.  The lowest-spatial- frequency data of Van Doorn and Koenderink at various temporal frequencies were matched against the sensitivities computed for 
spatially uniform temporal sine waves.  In each case, the vision-model field rate sampled the temporal sine wave at 50 and 60 Hz.
\par 
\par \tab }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\pict\wmetafile8\picw12136\pich9137\picwgoal6880\pichgoal5180 \piccropl-10\piccropr-10 
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fa0206000800000000006a002200040000002d0100000e00000024030500100170ff280188ff1001a0fff80088ff100170ff0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0000000000000000350000004201050000002800000008000000080000000100010000000000080000
00120b0000120b00000000000000000000d400000000000000aa00000055000000aa00000055000000aa00000055000000aa0000005500000030030f853c0100008a43323c02757d8d040000002d010300040000002d01020004000000f00100000e00000024030500580238fe700250fe580268fe400250fe580238fe0400
00002d01010004000000f001030009000000fa0206000800000000006a002200040000002d0100000e00000024030500580238fe700250fe580268fe400250fe580238fe0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0000000000000000350000004201050000002800000008
00000008000000010001000000000008000000120b0000120b00000000000000000000d400000000000000aa00000055000000aa00000055000000aa00000055000000aa0000005500000030030f853c0100008a43323c02757d8d040000002d010300040000002d01020004000000f00100000e00000024030500a0036800
b8038000a003980088038000a0036800040000002d01010004000000f001030009000000fa0206000800000000006a002200040000002d0100000e00000024030500a0036800b8038000a003980088038000a00368000b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0000000000
0000000500000009020000000010000000fb02b8ff0000000000009001000000000000002047656e6576610000040000002d0103000900000021050500302e30303100c0fc20fb0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000800000021050400302e3031
e8fe50fb0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000800000021050300302e3100100180fb0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0000000000000000070000002105010031003803c8fb0b00000026
060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000800000021050400302e3031a803e8fb0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000800000021050300302e3100a80320fe0b00000026060f000c00ffff
ffff01000000000000000b00000026060f000c00ffffffff000000000000000007000000210501003100a80360000b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000007000000210502003130a80368020b00000026060f000c00ffffffff01000000000000000b
00000026060f000c00ffffffff0000000000000000080000002105030031303000a80370040b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000010000000fb02b8ff000000000000bc02000000000000002047656e6576610000040000002d01040004000000f001
0300120000002105170074656d706f72616c206672657175656e63792028487a2900400480fe0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000010000000fb02b8ff000084038403bc02000000000000002047656e6576610000040000002d01030004000000f0
0104000f00000021051200636f6e7472617374207468726573686f6c646f01f0fa0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000007000000fc020000ffffff000000040000002d010400040000002d01020004000000f00100000e00000024030500d0fcc0fc
a800c0fca80028fed0fc28fed0fcc0fc0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000500000009020000d40035000000420105000000280000000800000008000000010001000000000008000000120b0000120b00000000000000000000d4000000000000
00aa00000055000000aa00000055000000aa00000055000000aa000000550000008b4424048b4c2408a3cc00011c890d9c040000002d0100000e0000002403050080fdf0fc98fd08fd80fd20fd68fd08fd80fdf0fc040000002d01010004000000f001000009000000fa0206000800000000006a002200040000002d010000
0e0000002403050080fdf0fc98fd08fd80fd20fd68fd08fd80fdf0fc0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000500000009020000000010000000fb02b8ff0000000000009001000000000000002047656e6576610000040000002d01050004000000f0
0103000c00000021050b0056442026204b20646174610020fd28fe0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000009000000fa02060010000000008011002200040000002d01030004000000f001000005000000140268fdecfc05000000130268fd14fe0b00
000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000e00000021050f004a4e44204d6f64656c20363020487a0090fd28fe0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0000000000000000050000001402d8fdecfc050000
001302d8fd14fd0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0000000000000000050000001402d8fd4cfd050000001302d8fd74fd0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0000000000000000050000001402d8fdacfd0500
00001302d8fdd4fd0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000e00000021050f004a4e44204d6f64656c20353020487a0000fe28fe0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff01000000000000000b0000
0026060f000c00ffffffff0100000000000000040000002701ffff0300000000000000}}}{
\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Ref371770810}{\*\bkmkstart _Toc371771269}{\*\bkmkstart _Toc371773617}{\*\bkmkstart _Toc371868561}{\*\bkmkstart _Toc371869214}
{\*\bkmkstart _Toc371950216}{\*\bkmkstart _Toc371960408}{\*\bkmkstart _Toc371996778}{\*\bkmkstart _Toc373146356}{\*\bkmkstart _Toc373148430}{\*\bkmkstart _Toc373151197}{\*\bkmkstart _Toc374349662}{\*\bkmkstart _Toc394995865}Figure 8
{\*\bkmkend _Ref371770810}. Luma Temporal Sensitivity{\*\bkmkend _Toc371771269}{\*\bkmkend _Toc371773617}{\*\bkmkend _Toc371868561}{\*\bkmkend _Toc371869214}{\*\bkmkend _Toc371950216}{\*\bkmkend _Toc371960408}{\*\bkmkend _Toc371996778}
{\*\bkmkend _Toc373146356}{\*\bkmkend _Toc373148430}{\*\bkmkend _Toc373151197}{\*\bkmkend _Toc374349662}{\*\bkmkend _Toc394995865}
\par }\pard\plain \s3\sb120\sa120\keepn\nowidctlpar\widctlpar\outlinelevel2\adjustright \b\f44\cgrid {\b0 {\*\bkmkstart _Toc370034631}{\*\bkmkstart _Toc370042353}{\*\bkmkstart _Toc370044458}{\*\bkmkstart _Toc370641499}{\*\bkmkstart _Toc370641838}
{\*\bkmkstart _Toc371344651}{\*\bkmkstart _Toc371422824}{\*\bkmkstart _Toc371429464}{\*\bkmkstart _Toc371432502}{\*\bkmkstart _Toc371473035}{\*\bkmkstart _Toc371691685}{\*\bkmkstart _Toc371773756}{\*\bkmkstart _Toc371868440}{\*\bkmkstart _Toc371950119}
{\*\bkmkstart _Toc371960275}{\*\bkmkstart _Toc371996523}{\*\bkmkstart _Toc374349535}{\*\bkmkstart _Toc394995850}3.1.3\tab }{Adjustment of masking constants{\*\bkmkend _Toc370034631}{\*\bkmkend _Toc370042353}{\*\bkmkend _Toc370044458}
{\*\bkmkend _Toc370641499}{\*\bkmkend _Toc370641838}{\*\bkmkend _Toc371344651}{\*\bkmkend _Toc371422824}{\*\bkmkend _Toc371429464}{\*\bkmkend _Toc371432502}{\*\bkmkend _Toc371473035}{\*\bkmkend _Toc371691685}{\*\bkmkend _Toc371773756}
{\*\bkmkend _Toc371868440}{\*\bkmkend _Toc371950119}{\*\bkmkend _Toc371960275}{\*\bkmkend _Toc371996523}{\*\bkmkend _Toc374349535}{\*\bkmkend _Toc394995850}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab The masking-parameter 
values were fit by comparing predictions for masked contrast discrimination with data acquired by Carlson and Cohen (1978).  The results of the final-fit comparison appear in Figure 9.   From the Carlson-Cohen study, a single observer's data was chosen su
b
ject to the criteria of being representative and also of having sufficient data points.  In this case, the model stimulus consisted of a spatial sine wave of given pedestal contrast in both test and reference fields, and additionally a contrast increment 
of the test-field sine wave.  The contrast-increment necessary to achieve 1 JND was determined from the model for each contrast-pedestal value, and then plotted in Figure 9.  
\par 
\par \tab }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\pict\wmetafile8\picw13264\pich9031\picwgoal7520\pichgoal5120 \piccropl-10\piccropr-10 
010009000003ef0900000600350000000000050000000b0238fcd8f9050000000c020008c00b0400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff00000000000000000b00000026060f000c00ffffffff000000
00000000000b00000026060f000c00ffffffff000000000000000009000000fa02060008000000000000002200040000002d0100000500000014027cfc94fb050000001302ec0294fb0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0000000000000000050000001402ec027cfb
050000001302ec02acfb0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0000000000000000050000001402b4ff7cfb050000001302b4ffacfb0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000500000014027cfc7c
fb0500000013027cfcacfb0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0000000000000000050000001402ec0294fb050000001302ec0244050b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000500000014020803
90fb050000001302d80290fb0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000500000014020803c8fe050000001302d802c8fe0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000005000000140208
030802050000001302d80208020b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000005000000140208034005050000001302d80240050b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000009000000fa02
060010000000008011002200040000002d01010004000000f00100001800000025030a0020fcc800d0fcd001a0fd600248fe3002d0fef00150ff980108003001d800a000980268ff880448fe0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000005000000010200
0000000500000009020000d40035000000420105000000280000000800000008000000010001000000000008000000120b0000120b00000000000000000000d400000000000000aa00000055000000aa00000055000000aa00000055000000aa0000005500000000002503030000003801180038012000040000002d010000
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fcb00038fcc80020fce00008fcc80020fcb0000b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000035000000420105000000280000000800000008000000010001000000000008000000120b0000120b00000000000000000000d400000000000000aa0000005500
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00040000002d0100000e00000024030500d0fca001e8fcb801d0fcd001b8fcb801d0fca0010b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000035000000420105000000280000000800000008000000010001000000000008000000120b0000120b000000000000
00000000d400000000000000aa00000055000000aa00000055000000aa00000055000000aa0000005500000000000000050000001402f1fec0010500040000002d010300040000002d01020004000000f00100000e00000024030500a0fdf001b8fd0802a0fd200288fd0802a0fdf001040000002d01010004000000f00103
0009000000fa0206000800000000006a002200040000002d0100000e00000024030500a0fdf001b8fd0802a0fd200288fd0802a0fdf0010b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000035000000420105000000280000000800000008000000010001000000
000008000000120b0000120b00000000000000000000d400000000000000aa00000055000000aa00000055000000aa00000055000000aa0000005500000000000000050000001402f1fec0010500040000002d010300040000002d01020004000000f00100000e0000002403050048fe580260fe700248fe880230fe700248
fe5802040000002d01010004000000f001030009000000fa0206000800000000006a002200040000002d0100000e0000002403050048fe580260fe700248fe880230fe700248fe58020b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000035000000420105000000
280000000800000008000000010001000000000008000000120b0000120b00000000000000000000d400000000000000aa00000055000000aa00000055000000aa00000055000000aa000000550000008b442404a39836011cc3cccccccccccc040000002d010300040000002d01020004000000f00100000e000000240305
00d0fe0002e8fe1802d0fe3002b8fe1802d0fe0002040000002d01010004000000f001030009000000fa0206000800000000006a002200040000002d0100000e00000024030500d0fe0002e8fe1802d0fe3002b8fe1802d0fe00020b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff
000000000000000035000000420105000000280000000800000008000000010001000000000008000000120b0000120b00000000000000000000d400000000000000aa00000055000000aa00000055000000aa00000055000000aa00000055000000088b0d7836011cff0d7836011c85c975040000002d010300040000002d
01020004000000f00100000e0000002403050050ffb00168ffc80150ffe00138ffc80150ffb001040000002d01010004000000f001030009000000fa0206000800000000006a002200040000002d0100000e0000002403050050ffb00168ffc80150ffe00138ffc80150ffb0010b00000026060f000c00ffffffff01000000
000000000b00000026060f000c00ffffffff000000000000000035000000420105000000280000000800000008000000010001000000000008000000120b0000120b00000000000000000000d400000000000000aa00000055000000aa00000055000000aa00000055000000aa00000055000000088b0d7836011cff0d7836
011c85c975040000002d010300040000002d01020004000000f00100000e00000024030500080048012000600108007801f0ff600108004801040000002d01010004000000f001030009000000fa0206000800000000006a002200040000002d0100000e00000024030500080048012000600108007801f0ff600108004801
0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000035000000420105000000280000000800000008000000010001000000000008000000120b0000120b00000000000000000000d400000000000000aa00000055000000aa00000055000000aa00000055000000aa
0000005500000036011c7e208b0da836011c83c2084601040000002d010300040000002d01020004000000f00100000e00000024030500d8008800f000a000d800b800c000a000d8008800040000002d01010004000000f001030009000000fa0206000800000000006a002200040000002d0100000e00000024030500d800
8800f000a000d800b800c000a000d80088000b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000035000000420105000000280000000800000008000000010001000000000008000000120b0000120b00000000000000000000d400000000000000aa000000550000
00aa00000055000000aa00000055000000aa000000550000000000007405b80100000085c07439833d040000002d010300040000002d01020004000000f00100000e00000024030500980238ffb00250ff980268ff800250ff980238ff040000002d01010004000000f001030009000000fa0206000800000000006a002200
040000002d0100000e00000024030500980238ffb00250ff980268ff800250ff980238ff0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000035000000420105000000280000000800000008000000010001000000000008000000120b0000120b00000000000000
000000d400000000000000aa00000055000000aa00000055000000aa00000055000000aa000000550000000000007405b80100000085c07439833d040000002d010300040000002d01020004000000f00100000e000000240305008804b8fda004d0fd8804e8fd7004d0fd8804b8fd040000002d01010004000000f0010300
09000000fa0206000800000000006a002200040000002d0100000e000000240305008804b8fda004d0fd8804e8fd7004d0fd8804b8fd0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000500000009020000000010000000fb02b8ff0000000000009001000000
000000002047656e6576610000040000002d0103000900000021050500302e30303100080378fa0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000800000021050400302e3031d0ffa8fa0b00000026060f000c00ffffffff01000000000000000b0000002606
0f000c00ffffffff00000000000000000800000021050300302e310098fcd8fa0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000900000021050500302e30303100780328fb0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ff
ffffff00000000000000000800000021050400302e3031780378fe0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000800000021050300302e31007803d0010b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000
0000000007000000210501003100780328050b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000010000000fb02b8ff000000000000bc02000000000000002047656e6576610000040000002d01040004000000f00103000f00000021051100706564657374616c20
636f6e7472617374000004f0fe0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000010000000fb02b8ff000084038403bc02000000000000002047656e6576610000040000002d01030004000000f00104001400000021051c00636f6e7472617374207468726573
686f6c6420696e6372656d656e74300249fa0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000007000000fc020000ffffff000000040000002d010400040000002d01020004000000f00100000e0000002403050068fc58fda8ff58fda8ff50fe68fc50fe68fc58
fd0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000500000009020000d40035000000420105000000280000000800000008000000010001000000000008000000120b0000120b00000000000000000000d400000000000000aa00000055000000aa0000005500
0000aa00000055000000aa00000055000000568b7424083935c836011c7418e86ef7040000002d0100000e00000024030500e8fc88fd00fda0fde8fcb8fdd0fca0fde8fc88fd040000002d01010004000000f001000009000000fa0206000800000000006a002200040000002d0100000e00000024030500e8fc88fd00fda0
fde8fcb8fdd0fca0fde8fc88fd0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff00000000000000000500000009020000000010000000fb02b8ff0000000000009001000000000000002047656e6576610000040000002d01050004000000f00103000e00000021050f003320632f
642050696361206461746100b8fd60fd0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff000000000000000009000000fa02060010000000008011002200040000002d01030004000000f001000005000000140200fe84fc05000000130200fe4cfd0b00000026060f000c00ffffff
ff01000000000000000b00000026060f000c00ffffffff00000000000000000b000000210509004a4e44204d6f64656c0028fe60fd0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0100000000000000040000002701ffff
0300000000000000}}}{
\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Toc371771270}{\*\bkmkstart _Ref371772185}{\*\bkmkstart _Toc371773618}{\*\bkmkstart _Toc371868562}{\*\bkmkstart _Toc371869215}
{\*\bkmkstart _Toc371950217}{\*\bkmkstart _Toc371960409}{\*\bkmkstart _Toc371996779}{\*\bkmkstart _Toc373146357}{\*\bkmkstart _Toc373148431}{\*\bkmkstart _Toc373151198}{\*\bkmkstart _Toc374349663}{\*\bkmkstart _Toc394995866}Figure 9
{\*\bkmkend _Ref371772185}. Luma Contrast Discrimination{\*\bkmkend _Toc371771270}{\*\bkmkend _Toc371773618}{\*\bkmkend _Toc371868562}{\*\bkmkend _Toc371869215}{\*\bkmkend _Toc371950217}{\*\bkmkend _Toc371960409}{\*\bkmkend _Toc371996779}
{\*\bkmkend _Toc373146357}{\*\bkmkend _Toc373148431}{\*\bkmkend _Toc373151198}{\*\bkmkend _Toc374349663}{\*\bkmkend _Toc394995866}
\par }\pard\plain \s2\sb120\sa120\keepn\nowidctlpar\widctlpar\outlinelevel1\adjustright \b\f44\fs28\cgrid {\b0 {\*\bkmkstart _Toc368828623}{\*\bkmkstart _Toc369224817}{\*\bkmkstart _Toc369249834}{\*\bkmkstart _Toc369436860}{\*\bkmkstart _Toc369915643}
{\*\bkmkstart _Toc370034632}{\*\bkmkstart _Toc370042354}{\*\bkmkstart _Toc370044459}{\*\bkmkstart _Toc370641500}{\*\bkmkstart _Toc370641839}{\*\bkmkstart _Toc371344652}{\*\bkmkstart _Toc371422825}{\*\bkmkstart _Toc371429465}{\*\bkmkstart _Toc371432503}
{\*\bkmkstart _Toc371473036}{\*\bkmkstart _Toc371691686}{\*\bkmkstart _Toc371773757}{\*\bkmkstart _Toc371868441}{\*\bkmkstart _Toc371950120}{\*\bkmkstart _Toc371960276}{\*\bkmkstart _Toc371996524}{\*\bkmkstart _Toc374349536}{\*\bkmkstart _Toc394995851}3.2
\tab }{Prediction{\*\bkmkend _Toc368828623}{\*\bkmkend _Toc369224817}{\*\bkmkend _Toc369249834}{\*\bkmkend _Toc369436860}{\*\bkmkend _Toc369915643}{\*\bkmkend _Toc370034632}{\*\bkmkend _Toc370042354}{\*\bkmkend _Toc370044459}{\*\bkmkend _Toc370641500}
{\*\bkmkend _Toc370641839}{\*\bkmkend _Toc371344652}{\*\bkmkend _Toc371422825}{\*\bkmkend _Toc371429465}{\*\bkmkend _Toc371432503}{\*\bkmkend _Toc371473036}{\*\bkmkend _Toc371691686}{\*\bkmkend _Toc371773757}{\*\bkmkend _Toc371868441}
{\*\bkmkend _Toc371950120}{\*\bkmkend _Toc371960276}{\*\bkmkend _Toc371996524}{\*\bkmkend _Toc374349536}{\*\bkmkend _Toc394995851}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab 
After model calibration, model predictions were compared with detection and discrimination data from stimuli that were not sine waves.  This was done in order to check the transferability of the sine-wave results to more general stimuli.  It will be se
en from Figures 10, 11, and 12 that the predictions were not applied to patterns with nominal spatial frequencies above 10 cycles/deg.  Such patterns would have had appreciable energies at spatial frequencies above 15 cycles/deg, and would have aliased wi
th the pixel sampling rate (30 samples per degree - see System Overview).
\par \tab In the first study (Figure 10), low-contrast disks in the test field were detected against a uniform reference field.  The experimental data are from Blackwell and Blackwell (1971). 
 In running the model for this particular study, it was necessary to replace the spatial summary measure with a maximum.  Otherwise the JND result was sensitive to the size of the background of the disk (i.e., to image size).
\par 
\par \tab \tab }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\pict\wmetafile8\picw8502\pich7197\picwgoal4820\pichgoal4080 \piccropl-10\piccropr-10 
010009000003f00700000600350000000000050000000b0218fd38fc050000000c02600688070400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff00000000000000000b00000026060f000c00ffffffff000000
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\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Ref371771636}{\*\bkmkstart _Toc371773619}{\*\bkmkstart _Toc371868563}{\*\bkmkstart _Toc371869216}{\*\bkmkstart _Toc371950218}
{\*\bkmkstart _Toc371960410}{\*\bkmkstart _Toc371996780}{\*\bkmkstart _Toc373146358}{\*\bkmkstart _Toc373148432}{\*\bkmkstart _Toc373151199}{\*\bkmkstart _Toc374349664}{\*\bkmkstart _Toc394995867}Figure 10{\*\bkmkend _Ref371771636}. Disk Detection
{\*\bkmkend _Toc371773619}{\*\bkmkend _Toc371868563}{\*\bkmkend _Toc371869216}{\*\bkmkend _Toc371950218}{\*\bkmkend _Toc371960410}{\*\bkmkend _Toc371996780}{\*\bkmkend _Toc373146358}{\*\bkmkend _Toc373148432}{\*\bkmkend _Toc373151199}
{\*\bkmkend _Toc374349664}{\*\bkmkend _Toc394995867}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab 
In the second study (Figure 11), the detection of a low-amplitude checkerboard, the data was acquired in an unpublished study at Sarnoff.  The third study (data from Carlson and Cohen, 1980) was somewhat different from the first
 two.  A blurred edge given by erf(ax) was presented in the reference image, and discrimination was attempted against an edge given by erf(a'x) in the test image.   Here, x is retinal distance in visual degrees, a = }{\pard\plain \s15\sa60\sl360\slmult0
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020000020000005053796d626f6c0000040000002d01000007000000210501007000070001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn4 {\pict\wmetafile8\picw212\pich191\picwgoal200\pichgoal180 \piccropl-10\piccropr-10 
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010009000003640000000100100000000000050000000b0200000000050000000c0209000a000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900102
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{\object\objemb\rsltmerge\objw220\objh220\objcropl-10\objcropr-10{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000000000000c00000002000003010a01028544000001050000050000000d0000004d45544146494c455049435400e9000000
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000000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn2 {\pict\wmetafile8\picw233\pich233\picwgoal220\pichgoal220 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900100
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000000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn2 {\pict\wmetafile8\picw233\pich233\picwgoal220\pichgoal220 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900100
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\s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\dn2\cgrid {\object\objemb\rsltmerge\objw220\objh220\objcropl-10\objcropr-10{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000000000000c000000
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000000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn2 {\pict\wmetafile8\picw233\pich233\picwgoal220\pichgoal220 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900100
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\par \tab  It can be seen that the model predictions are well fit to the data, for the range of spatial frequencies characteristic of the display at the four-screen-height viewing distance.
\par 
\par }\pard \s15\sa60\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright {\tab \tab }{\pard\plain \s15\sa60\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\pict\wmetafile8\picw8961\pich7620\picwgoal5080\pichgoal4320 
\piccropl-10\piccropr-10 
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\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Ref371771967}{\*\bkmkstart _Toc371773620}{\*\bkmkstart _Toc371868564}{\*\bkmkstart _Toc371869217}{\*\bkmkstart _Toc371950219}
{\*\bkmkstart _Toc371960411}{\*\bkmkstart _Toc371996781}{\*\bkmkstart _Toc373146359}{\*\bkmkstart _Toc373148433}{\*\bkmkstart _Toc373151200}{\*\bkmkstart _Toc374349665}{\*\bkmkstart _Toc394995868}Figure 11{\*\bkmkend _Ref371771967}. Checkerboard Detection
{\*\bkmkend _Toc371773620}{\*\bkmkend _Toc371868564}{\*\bkmkend _Toc371869217}{\*\bkmkend _Toc371950219}{\*\bkmkend _Toc371960411}{\*\bkmkend _Toc371996781}{\*\bkmkend _Toc373146359}{\*\bkmkend _Toc373148433}{\*\bkmkend _Toc373151200}
{\*\bkmkend _Toc374349665}{\*\bkmkend _Toc394995868}
\par }\pard\plain \s31\qj\li720\ri720\sb120\sa300\sl360\slmult0\nowidctlpar\widctlpar\adjustright \b\f44\cgrid {
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\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Ref371772607}{\*\bkmkstart _Toc371773621}{\*\bkmkstart _Toc371868565}{\*\bkmkstart _Toc371869218}{\*\bkmkstart _Toc371950220}
{\*\bkmkstart _Toc371960412}{\*\bkmkstart _Toc371996782}{\*\bkmkstart _Toc373146360}{\*\bkmkstart _Toc373148434}{\*\bkmkstart _Toc373151201}{\*\bkmkstart _Toc374349666}{\*\bkmkstart _Toc394995869}Figure 12{\*\bkmkend _Ref371772607}
. Edge Sharpness Discrimination{\*\bkmkend _Toc371773621}{\*\bkmkend _Toc371868565}{\*\bkmkend _Toc371869218}{\*\bkmkend _Toc371950220}{\*\bkmkend _Toc371960412}{\*\bkmkend _Toc371996782}{\*\bkmkend _Toc373146360}{\*\bkmkend _Toc373148434}
{\*\bkmkend _Toc373151201}{\*\bkmkend _Toc374349666}{\*\bkmkend _Toc394995869}
\par }\pard\plain \s1\sb240\sa180\keepn\pagebb\nowidctlpar\widctlpar\outlinelevel0\adjustright \b\f44\fs36\cgrid {\b0 {\*\bkmkstart _Ref371395834}{\*\bkmkstart _Toc371422826}{\*\bkmkstart _Toc371429466}{\*\bkmkstart _Toc371432504}{\*\bkmkstart _Toc371473037}
{\*\bkmkstart _Toc371691687}{\*\bkmkstart _Toc371773758}{\*\bkmkstart _Toc371868442}{\*\bkmkstart _Toc371950121}{\*\bkmkstart _Toc371960277}{\*\bkmkstart _Toc371996525}{\*\bkmkstart _Toc374349537}{\*\bkmkstart _Toc394995852}4.\tab }{Chroma Calibration
{\*\bkmkend _Ref371395834}{\*\bkmkend _Toc371422826}{\*\bkmkend _Toc371429466}{\*\bkmkend _Toc371432504}{\*\bkmkend _Toc371473037}{\*\bkmkend _Toc371691687}{\*\bkmkend _Toc371773758}{\*\bkmkend _Toc371868442}{\*\bkmkend _Toc371950121}
{\*\bkmkend _Toc371960277}{\*\bkmkend _Toc371996525}{\*\bkmkend _Toc374349537}{\*\bkmkend _Toc394995852}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab As in luma-parameter calibration, psychophysical data were used to calibrate chroma parameters (i.e., to adj
ust their values for best model fits).  In all cases, the stimuli were four equal fields, injected into the model as images in CIE X, Y, and Z just prior to conversion to CIELUV.
\par }\pard\plain \s2\sb120\sa120\keepn\nowidctlpar\widctlpar\outlinelevel1\adjustright \b\f44\fs28\cgrid {\b0 {\*\bkmkstart _Toc371473039}{\*\bkmkstart _Toc371691689}{\*\bkmkstart _Toc371773760}{\*\bkmkstart _Toc371868443}{\*\bkmkstart _Toc371950122}
{\*\bkmkstart _Toc371960278}{\*\bkmkstart _Toc371996526}{\*\bkmkstart _Toc374349538}{\*\bkmkstart _Toc394995853}4.1\tab }{Adjustment of contrast-normalization constants{\*\bkmkend _Toc371473039}{\*\bkmkend _Toc371691689}{\*\bkmkend _Toc371773760}
{\*\bkmkend _Toc371868443}{\*\bkmkend _Toc371950122}{\*\bkmkend _Toc371960278}{\*\bkmkend _Toc371996526}{\*\bkmkend _Toc374349538}{\*\bkmkend _Toc394995853}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab The model predictions for
 chromatic contrast sensitivities prior to masking were matched to contrast-sensitivity data presented by Mullen (1985).  The test sequences used  were four equal fields, each with a horizontally varying spatial sine-wave grating injected as (X, Y, Z) val
ues.  The data used for calibration were from Mullen's Figure 6,  corresponding to which each test image was a red-green isoluminous sine-wave.  At  pixel i, the test-image sine wave had tristimulus values given by 
\par 
\par }\pard\plain \s42\li720\nowidctlpar\widctlpar\tqr\tx7920\adjustright \f44\cgrid {X(i) = (Y}{\dn4 o}{/2) \{(x}{\dn4 r}{/y}{\dn4 r}{ + x}{\dn4 g}{/y}{\dn4 g}{) + cos( 2}{\pard\plain \s42\li720\nowidctlpar\widctlpar\tqr\tx7920\adjustright \f44\dn4\cgrid 
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010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900100
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\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {
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\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {
\par }\pard\plain \s42\li720\nowidctlpar\widctlpar\tqr\tx7920\adjustright \f44\cgrid {Z(i) = (Yo/2) \{(zr/yr + zg/yg) + cos(  2}{\pard\plain \s42\li720\nowidctlpar\widctlpar\tqr\tx7920\adjustright \f44\dn4\cgrid {\object\objemb\rsltmerge\objw200\objh180
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020000020000005053796d626f6c0000040000002d01000007000000210501007000070001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn4 {\pict\wmetafile8\picw212\pich191\picwgoal200\pichgoal180 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c0209000a000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900102
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{\object\objemb\rsltmerge\objw220\objh220\objcropl-10\objcropr-10{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000000000000c00000002000003010a01028544000001050000050000000d0000004d45544146494c455049435400e9000000
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000000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn2 {\pict\wmetafile8\picw233\pich233\picwgoal220\pichgoal220 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900100
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\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {
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000000000c00000002000003010a01028544000001050000050000000d0000004d45544146494c455049435400e900000017ffffffd00000000800e900e9000000
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000000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn2 {\pict\wmetafile8\picw233\pich233\picwgoal220\pichgoal220 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900100
0000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}}}}}{m is the threshold incremental discrimination contrast, (x}{\dn4 r}{, y}{\dn4 r}{
) = (.636, .364) is the chromaticity of the red interference filter (at 602 nm) , (x}{\dn4 g}{, y}{\dn4 g}{) = (.122, .823) is the chromaticity of the green interference filter (at 526 nm), z}{\dn4 r}{ = 1 - x}{\dn4 r}{ - y}{\dn4 r}{,  z}{\dn4 g}{ = 1 - x
}{\dn4 g}{ - y}{\dn4 g}{, and a = .03 deg/pixel .  The reference-image is a uniform field represented by Equation (1) but with }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\dn2\cgrid {\object\objemb\rsltmerge\objw220\objh220
\objcropl-10\objcropr-10{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000000000000c00000002000003010a01028544000001050000050000000d0000004d45544146494c455049435400e900000017ffffffd00000000800e900e9000000
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff0000000000009001
000000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn2 {\pict\wmetafile8\picw233\pich233\picwgoal220\pichgoal220 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900100
0000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}}}}}{m = 0.   For purposes of the model, it is sufficient to set Y}{\dn4 o}{ = 1.
\par \tab To generate points on the model-based curve, the above stimulus was presented at various values of f, and the contrast threshold }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\dn2\cgrid {\object\objemb\rsltmerge
\objw220\objh220\objcropl-10\objcropr-10{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000000000000c00000002000003010a01028544000001050000050000000d0000004d45544146494c455049435400e900000017ffffffd0000000
0800e900e9000000
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000000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn2 {\pict\wmetafile8\picw233\pich233\picwgoal220\pichgoal220 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900100
0000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}}}}}{m for 1 JND output was assessed.  The fit of modeled ch
romatic-contrast sensitivity to data (see Figure 13 for final fit) was used to adjust the constrast-sensitivity parameters in the model.  
\par \tab }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\pict\wmetafile8\picw11853\pich8220\picwgoal6720\pichgoal4660 \piccropl-10\piccropr-10 
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\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Ref371773400}{\*\bkmkstart _Toc371773622}{\*\bkmkstart _Toc371868567}{\*\bkmkstart _Toc371869219}{\*\bkmkstart _Toc371950221}
{\*\bkmkstart _Toc371960413}{\*\bkmkstart _Toc371996783}{\*\bkmkstart _Toc373146361}{\*\bkmkstart _Toc373148435}{\*\bkmkstart _Toc373151202}{\*\bkmkstart _Toc374349667}{\*\bkmkstart _Toc394995870}Figure 13{\*\bkmkend _Ref371773400}
. Chroma Spatial Sensitivity{\*\bkmkend _Toc371773622}{\*\bkmkend _Toc371868567}{\*\bkmkend _Toc371869219}{\*\bkmkend _Toc371950221}{\*\bkmkend _Toc371960413}{\*\bkmkend _Toc371996783}{\*\bkmkend _Toc373146361}{\*\bkmkend _Toc373148435}
{\*\bkmkend _Toc373151202}{\*\bkmkend _Toc374349667}{\*\bkmkend _Toc394995870}
\par }\pard\plain \s2\sb120\sa120\keepn\nowidctlpar\widctlpar\outlinelevel1\adjustright \b\f44\fs28\cgrid {\b0 {\*\bkmkstart _Toc371473040}{\*\bkmkstart _Toc371691690}{\*\bkmkstart _Toc371773761}{\*\bkmkstart _Toc371868444}{\*\bkmkstart _Toc371950123}
{\*\bkmkstart _Toc371960279}{\*\bkmkstart _Toc371996527}{\*\bkmkstart _Toc374349539}{\*\bkmkstart _Toc394995854}4.2\tab }{Adjustment of masking constants{\*\bkmkend _Toc371473040}{\*\bkmkend _Toc371691690}{\*\bkmkend _Toc371773761}
{\*\bkmkend _Toc371868444}{\*\bkmkend _Toc371950123}{\*\bkmkend _Toc371960279}{\*\bkmkend _Toc371996527}{\*\bkmkend _Toc374349539}{\*\bkmkend _Toc394995854}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab The model pre
dictions for chroma masking were matched to data presented by Switkes. et al. (1988).  The test sequences used  were four equal fields, each with a horizontally varying spatial sine-wave grating injected as (X, Y, Z) values.  }{\i  }{
To correspond with Figure 4  of that work (chroma masking of chroma), at pixel i, the test-image sine wave had tristimulus values given by 
\par 
\par }\pard\plain \s42\li720\nowidctlpar\widctlpar\tqr\tx7920\adjustright \f44\cgrid {X(i) = (Y}{\dn4 o}{/2) \{(x}{\dn4 r}{/y}{\dn4 r}{ + x}{\dn4 g}{/y}{\dn4 g}{) + cos(  2}{\pard\plain \s42\li720\nowidctlpar\widctlpar\tqr\tx7920\adjustright \f44\dn4\cgrid 
{\object\objemb\rsltmerge\objw200\objh180\objcropl-10\objcropr-10{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000000000000c00000002000003010a01028470000001050000050000000d0000004d45544146494c455049435400d4000000
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020000020000005053796d626f6c0000040000002d01000007000000210501007000070001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn4 {\pict\wmetafile8\picw212\pich191\picwgoal200\pichgoal180 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c0209000a000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900102
0000020000005053796d626f6c0000040000002d01000007000000210501007000070001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}}}}}{f a i) [(m}{\dn4  }{+}{\dn4  }{\pard\plain \s42\li720\nowidctlpar\widctlpar\tqr\tx7920\adjustright 
\f44\dn2\cgrid {\object\objemb\rsltmerge\objw220\objh220\objcropl-10\objcropr-10{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000000000000c00000002000003010a01028544000001050000050000000d000000
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000000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn2 {\pict\wmetafile8\picw233\pich233\picwgoal220\pichgoal220 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900100
0000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}}}}}{m)(x}{\dn4 r}{/y}{\dn4 r}{ - x}{\dn4 g}{/y}{\dn4 g}{)]\}
\par 
\par {\*\bkmkstart _Toc371868568}Y(i) = Y}{\dn4 o}{\tab ( 2){\*\bkmkend _Toc371868568}
\par 
\par Z(i) = (Y}{\dn4 o}{/2) \{(z}{\dn4 r}{/y}{\dn4 r}{ + z}{\dn4 g}{/y}{\dn4 g}{) + cos( 2}{\pard\plain \s42\li720\nowidctlpar\widctlpar\tqr\tx7920\adjustright \f44\dn4\cgrid {\object\objemb\rsltmerge\objw200\objh180\objcropl-10\objcropr-10
{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000000000000c00000002000003010a01028470000001050000050000000d0000004d45544146494c455049435400d400000041ffffffd00000000800d400bf000000
010009000003640000000100100000000000050000000b0200000000050000000c0209000a000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff0000000000009001
020000020000005053796d626f6c0000040000002d01000007000000210501007000070001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn4 {\pict\wmetafile8\picw212\pich191\picwgoal200\pichgoal180 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c0209000a000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900102
0000020000005053796d626f6c0000040000002d01000007000000210501007000070001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}}}}}{f a i) [(m}{\dn4  }{+}{\dn4  }{\pard\plain \s42\li720\nowidctlpar\widctlpar\tqr\tx7920\adjustright 
\f44\dn2\cgrid {\object\objemb\rsltmerge\objw220\objh220\objcropl-10\objcropr-10{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000000000000c00000002000003010a01028544000001050000050000000d000000
4d45544146494c455049435400e900000017ffffffd00000000800e900e9000000
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff0000000000009001
000000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn2 {\pict\wmetafile8\picw233\pich233\picwgoal220\pichgoal220 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900100
0000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}}}}}{m) (z}{\dn4 r}{/y}{\dn4 r}{ - z}{\dn4 g}{/y}{\dn4 g}{)]\},
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {
\par where }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\dn2\cgrid {\object\objemb\rsltmerge\objw220\objh220\objcropl-10\objcropr-10{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000
000000000c00000002000003010a01028544000001050000050000000d0000004d45544146494c455049435400e900000017ffffffd00000000800e900e9000000
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff0000000000009001
000000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn2 {\pict\wmetafile8\picw233\pich233\picwgoal220\pichgoal220 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900100
0000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}}}}}{m is the threshold incremental discrimination contrast, (x}{\dn4 r}{, y}{\dn4 r}{
) = (.580, .362) is the chromaticity of the red phosphor, (x}{\dn4 g}{, y}{\dn4 g}{) = (.301, .589) is the chromaticity of the green phosphor, z}{\dn4 r}{ = 1 - x}{\dn4 r}{ - y}{\dn4 r}{,  z}{\dn4 g}{ = 1 - x}{\dn4 g}{ - y}{\dn4 g}{
, and f a = 2 c/deg * .03 deg/pixel = .06. The reference-image sine wave is the same as the test-image sine wave but with }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\dn2\cgrid {\object\objemb\rsltmerge\objw220\objh220
\objcropl-10\objcropr-10{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000000000000c00000002000003010a01028544000001050000050000000d0000004d45544146494c455049435400e900000017ffffffd00000000800e900e9000000
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff0000000000009001
000000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn2 {\pict\wmetafile8\picw233\pich233\picwgoal220\pichgoal220 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900100
0000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}}}}}{m = 0. For purposes of the model, it is sufficient to set Y}{\dn4 o}{ = 1.
\par \tab To generate points on the model-based curve, the above stimulus was presented at various values of mask contrast m, and the contrast threshold }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\dn2\cgrid {\object\objemb
\rsltmerge\objw220\objh220\objcropl-10\objcropr-10{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000000000000c00000002000003010a01028544000001050000050000000d0000004d45544146494c455049435400e900000017ffffffd0000000
0800e900e9000000
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff0000000000009001
000000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}{\result {\dn2 {\pict\wmetafile8\picw233\pich233\picwgoal220\pichgoal220 \piccropl-10\piccropr-10 
010009000003640000000100100000000000050000000b0200000000050000000c020b000b000400000004010d00040000002e011800040000000201010005000000090200000000050000000102ffffff00030000001e000b00000026060f000c00ffffffff000000000000000010000000fb02f4ff000000000000900100
0000020000005053796d626f6c0000040000002d010000070000002105010044000a0001000b00000026060f000c00ffffffff0100000000000000040000002701ffff030000000000}}}}}{
m for 1 JND output was assessed.  The fit of modeled chromatic-contrast sensitivity to data (see Figure 14 for final fit) was used to adjust the chromatic transducer parameters in the model.  
\par 
\par \tab }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\pict\wmetafile8\picw10654\pich9878\picwgoal6040\pichgoal5600 \piccropl-10\piccropr-10 
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0f000c00ffffffff00000000000000000b000000210509004a4e44204d6f64656c0030fe70fe0b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff01000000000000000b00000026060f000c00ffffffff0100000000000000040000002701ffff0300000000000000}}}{
\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Ref371773521}{\*\bkmkstart _Toc371773623}{\*\bkmkstart _Toc371868569}{\*\bkmkstart _Toc371869220}{\*\bkmkstart _Toc371950222}
{\*\bkmkstart _Toc371960414}{\*\bkmkstart _Toc371996784}{\*\bkmkstart _Toc373146362}{\*\bkmkstart _Toc373148436}{\*\bkmkstart _Toc373151203}{\*\bkmkstart _Toc374349668}{\*\bkmkstart _Toc394995871}Figure 14{\*\bkmkend _Ref371773521}
.  Chroma Contrast Discrimination{\*\bkmkend _Toc371773623}{\*\bkmkend _Toc371868569}{\*\bkmkend _Toc371869220}{\*\bkmkend _Toc371950222}{\*\bkmkend _Toc371960414}{\*\bkmkend _Toc371996784}{\*\bkmkend _Toc373146362}{\*\bkmkend _Toc373148436}
{\*\bkmkend _Toc373151203}{\*\bkmkend _Toc374349668}{\*\bkmkend _Toc394995871}
\par }\pard\plain \s1\sb240\sa180\keepn\pagebb\nowidctlpar\widctlpar\outlinelevel0\adjustright \b\f44\fs36\cgrid {\b0 {\*\bkmkstart _Ref371395886}{\*\bkmkstart _Toc371422827}{\*\bkmkstart _Toc371429474}{\*\bkmkstart _Toc371432512}{\*\bkmkstart _Toc371473045}
{\*\bkmkstart _Toc371691695}{\*\bkmkstart _Toc371773766}{\*\bkmkstart _Toc371868445}{\*\bkmkstart _Toc371950124}{\*\bkmkstart _Toc371960280}{\*\bkmkstart _Toc371996528}{\*\bkmkstart _Toc374349540}{\*\bkmkstart _Toc394995855}5.\tab }{
Comparisons with Rating Data{\*\bkmkend _Ref371395886}{\*\bkmkend _Toc371422827}{\*\bkmkend _Toc371429474}{\*\bkmkend _Toc371432512}{\*\bkmkend _Toc371473045}{\*\bkmkend _Toc371691695}{\*\bkmkend _Toc371773766}{\*\bkmkend _Toc371868445}
{\*\bkmkend _Toc371950124}{\*\bkmkend _Toc371960280}{\*\bkmkend _Toc371996528}{\*\bkmkend _Toc374349540}{\*\bkmkend _Toc394995855}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\b \tab }{Four image sequences, each with various degrees of distortion, were used to compare the Sarnoff Vision Model with DSCQS
 rating data collected by an ISO/IEC  group on high bit-rate (20 to 50 mbits/sec) MPEG-2 sequences that had been subjected to different numbers of compression and reconstruction, both with and without intervening spatial and/or temporal shifts.  The resul
ts are plotted in Figure 15, and reveal a correlation 0.92 between the model and the data.  For each of the sequences, the Vision Model processed 30 fields.  
\par }\pard \s15\qc\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright {\pard\plain \s15\qc\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\object\objemb\rsltmerge\objw7421\objh5301\objcropl-10\objcropr-10{\*\objclass Word.Picture.8}
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\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Toc371868571}{\*\bkmkstart _Toc371869221}{\*\bkmkstart _Toc371950223}{\*\bkmkstart _Toc371960415}{\*\bkmkstart _Toc371996785}
{\*\bkmkstart _Toc373146363}{\*\bkmkstart _Toc373148437}{\*\bkmkstart _Toc373151204}{\*\bkmkstart _Toc374349669}{\*\bkmkstart _Ref392135151}{\*\bkmkstart _Ref392305627}{\*\bkmkstart _Toc394995872}Figure 15{\*\bkmkend _Ref392135151}. 
{\*\bkmkend _Toc371868571}{\*\bkmkend _Toc371869221}{\*\bkmkend _Toc371950223}{\*\bkmkend _Toc371960415}{\*\bkmkend _Toc371996785}{\*\bkmkend _Toc373146363}{\*\bkmkend _Toc373148437}{\*\bkmkend _Toc373151204}{\*\bkmkend _Toc374349669}
MPEG-2 Rating Predictions, 30 Fields Per Sequence.{\*\bkmkend _Ref392305627}{\*\bkmkend _Toc394995872}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Toc368828624}{\*\bkmkstart _Toc369224818}{\*\bkmkstart _Toc369249835}{\*\bkmkstart _Toc369436861}{\*\bkmkstart _Toc369915644}{\*\bkmkstart _Toc370034633}
{\*\bkmkstart _Toc370042355}{\*\bkmkstart _Toc370044460}{\*\bkmkstart _Toc370641501}{\*\bkmkstart _Toc370641840}{\*\bkmkstart _Toc371344653}{\*\bkmkstart _Toc371422828}{\*\bkmkstart _Toc371429475}{\*\bkmkstart _Toc371432513}{\*\bkmkstart _Toc371473046}
{\*\bkmkstart _Toc371691696}{\*\bkmkstart _Toc371773767}{\*\bkmkstart _Toc371868446}{\*\bkmkstart _Toc371950125}{\*\bkmkstart _Toc371960281}{\*\bkmkstart _Toc371996529}{\*\bkmkstart _Toc374349541}\tab 
In addition to these MPEG rating predictions, we have run the model on some lower bit rate MPEG-2 sequences (2 to 7 mbits/sec), and have rerun the model on some JPEG rating data first reported in Lubin, 1995.  For the MPEG-2 sequences, data were 
collected at Sarnoff under a different rating paradigm.  In this paradigm, subjects were shown, in each trial, five-second clips of the reference and then the test sequence, and were asked to rate the perceptibility of distortions using the following five
 point scale:
\par }\pard \s15\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright {\tab 0.\tab not perceptible
\par \tab 1.\tab barely perceptible
\par \tab 2.\tab mildly perceptible
\par \tab 3.\tab clearly perceptible
\par }\pard \s15\sl360\slmult0\nowidctlpar\widctlpar\adjustright {\tab 4.\tab extremely perceptible
\par }\pard \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright {Each data point is an average of at least 80 separate trials (20 subjects x 4 replications per subject).  Data were collected f
or five different sequences (as shown in the legend in Figure 16) at three bit-rates each, using a standard TM5 encoder.   Figure 16 shows the correlations of the JND Vision Model with these data.  For comparison purposes, Figure 17 shows the correlation 
of an MSE measure. 
\par }\pard\plain \s40\qc\sb120\sa120\keepn\nowidctlpar\widctlpar\adjustright \b\f44\cgrid {\pard\plain \s40\qc\sb120\sa120\keepn\nowidctlpar\widctlpar\adjustright \b\f44\cgrid {{\pict\wmetafile8\picw7549\pich6526\picwgoal4280\pichgoal3700 \box\brdrs\brdrw30 
\piccropl-10\piccropr-10 
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\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Ref394303836}{\*\bkmkstart _Toc394995873}Figure 16{\*\bkmkend _Ref394303836}.  MPEG-2 low bit-rate rating predictions{\*\bkmkend _Toc394995873} 

\par }\pard\plain \s40\qc\sb120\sa120\keepn\nowidctlpar\widctlpar\adjustright \b\f44\cgrid {\pard\plain \s40\qc\sb120\sa120\keepn\nowidctlpar\widctlpar\adjustright \b\f44\cgrid {{\pict\wmetafile8\picw7761\pich6526\picwgoal4400\pichgoal3700 \box\brdrs\brdrw30 
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\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Ref394304013}{\*\bkmkstart _Toc394995874}Figure 17{\*\bkmkend _Ref394304013}.  MSE predictions on low bit-rate MPEG-2 data.
{\*\bkmkend _Toc394995874}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab Note that, although MSE shows a monotonic relationship between quality 
and bit-rate for each image sequence, it does not adequately capture the differences in this relationship from one sequence to the next.  On the other hand, the JND Vision Model produces quite good correlation.
\par \tab For the JPEG task, observers were shown four different scenes (p1, p2, p3, and p4) each compressed at 11 different JPEG levels.  Observers were then asked to rate the quality of each resulting still image on a 100-point scale (100 being best).
\par \tab As shown in Figure 18, the model does a good job predic
ting the rating data, with excellent clustering across image types and a strong linear correlation over the entire rating range (.94).  Even better correlation (0.97) results when one omits the four points above 15 JNDs, for which some saturation at the l
ow end of the rating scale has evidently occurred.  
\par 
\par }{\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\pict\wmetafile8\picw11430\pich9349\picwgoal6480\pichgoal5300 \piccropl-10\piccropr-10 
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\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Ref378134509}{\*\bkmkstart _Toc394995875}Figure 18{\*\bkmkend _Ref378134509}. Predictions of Final Model on JPEG rating data
{\*\bkmkend _Toc394995875}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {\tab On the other hand, as shown in Figure 19, correlation among ratings and predictions based on the root mean-squared e
rror between the original and compressed images are not nearly as good (.81).  Here, the predictions do not track well across image types, even though a monotonic relation between rating and predicted value is observed within each image.
\par 
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\par }\pard\plain \s30\qc\sb120\sa120\sl360\slmult0\keepn\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart _Ref378134599}{\*\bkmkstart _Toc394995876}Figure 19{\*\bkmkend _Ref378134599}. RMS error predictions on JPEG rating data
{\*\bkmkend _Toc394995876}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {
\par }\pard\plain \s1\sb240\sa180\keepn\pagebb\nowidctlpar\widctlpar\outlinelevel0\adjustright \b\f44\fs36\cgrid {\b0 {\*\bkmkstart _Toc394995856}{\*\bkmkend _Toc368828624}{\*\bkmkend _Toc369224818}{\*\bkmkend _Toc369249835}{\*\bkmkend _Toc369436861}
{\*\bkmkend _Toc369915644}{\*\bkmkend _Toc370034633}{\*\bkmkend _Toc370042355}{\*\bkmkend _Toc370044460}{\*\bkmkend _Toc370641501}{\*\bkmkend _Toc370641840}{\*\bkmkend _Toc371344653}{\*\bkmkend _Toc371422828}{\*\bkmkend _Toc371429475}
{\*\bkmkend _Toc371432513}{\*\bkmkend _Toc371473046}{\*\bkmkend _Toc371691696}{\*\bkmkend _Toc371773767}{\*\bkmkend _Toc371868446}{\*\bkmkend _Toc371950125}{\*\bkmkend _Toc371960281}{\*\bkmkend _Toc371996529}{\*\bkmkend _Toc374349541}6.\tab }{Conclusions
{\*\bkmkend _Toc394995856}
\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {{\*\bkmkstart B_Toc364589445}{\*\bkmkstart B_Toc365961322}{\*\bkmkstart B_Toc364582553}{\*\bkmkstart _Toc368110040}{\*\bkmkstart _Toc368112823}{\*\bkmkstart _Toc368112874}
{\*\bkmkstart _Toc368112932}{\*\bkmkstart _Toc368117546}{\*\bkmkstart _Toc368117655}{\*\bkmkstart _Toc368197245}{\*\bkmkstart _Toc368387814}{\*\bkmkstart _Toc368388293}{\*\bkmkstart _Toc368388441}{\*\bkmkstart _Toc368548969}{\*\bkmkstart _Toc368622363}
{\*\bkmkstart _Toc368649276}{\*\bkmkstart _Toc368664773}{\*\bkmkstart _Toc368752787}{\*\bkmkstart _Toc368823967}{\*\bkmkstart _Toc368828626}{\*\bkmkstart _Toc369224820}{\*\bkmkstart _Toc369249837}{\*\bkmkstart _Toc369436863}{\*\bkmkstart _Toc369915646}
{\*\bkmkstart _Toc370034635}{\*\bkmkstart _Toc370042357}{\*\bkmkstart _Toc370044462}{\*\bkmkstart _Toc370641503}{\*\bkmkstart _Toc370641842}{\*\bkmkstart _Toc371344655}{\*\bkmkstart _Toc371422830}{\*\bkmkstart _Toc371429477}{\*\bkmkstart _Toc371432515}
{\*\bkmkstart _Toc371473048}{\*\bkmkstart _Toc371691698}{\*\bkmkstart _Toc371773769}{\*\bkmkstart _Toc371868448}{\*\bkmkstart _Toc371950127}{\*\bkmkstart _Toc371960283}{\*\bkmkstart _Toc371996531}{\*\bkmkstart _Toc374349543}{\*\bkmkend B_Toc364589443}
{\*\bkmkend B_Toc365961320}{\*\bkmkend B_Toc364582551}{\*\bkmkend _Toc368110038}{\*\bkmkend _Toc368112821}{\*\bkmkend _Toc368112870}{\*\bkmkend _Toc368112930}{\*\bkmkend _Toc368117544}{\*\bkmkend _Toc368117653}{\*\bkmkend _Toc368197243}
{\*\bkmkend _Toc368387812}{\*\bkmkend _Toc368388291}{\*\bkmkend _Toc368388439}{\*\bkmkend _Toc368548967}{\*\bkmkend _Toc368622361}{\*\bkmkend _Toc368649274}{\*\bkmkend _Toc368664771}{\*\bkmkend _Toc368752785}\tab 
As described in the above sections, the Sarnoff JND Vision Model is based on known physiological mechanisms of vision, and is carefully calibrated according to
 basic psychophysical data.  This methodology provides it with a great deal of robustness in predicting visibility of distortions, not only in MPEG-2 video, but in an extremely broad range of current and future video applications.  The excellent predictio
ns of the model across the range of data described in this document should provide confidence that this model is a useful tool for image quality metering applications.
\par 
\par }\pard\plain \s1\sb240\sa180\keepn\pagebb\nowidctlpar\widctlpar\outlinelevel0\adjustright \b\f44\fs36\cgrid {\b0 {\*\bkmkstart _Toc394995857}7.\tab }{References{\*\bkmkend B_Toc364589445}{\*\bkmkend B_Toc365961322}{\*\bkmkend B_Toc364582553}
{\*\bkmkend _Toc368110040}{\*\bkmkend _Toc368112823}{\*\bkmkend _Toc368112874}{\*\bkmkend _Toc368112932}{\*\bkmkend _Toc368117546}{\*\bkmkend _Toc368117655}{\*\bkmkend _Toc368197245}{\*\bkmkend _Toc368387814}{\*\bkmkend _Toc368388293}
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\par }\pard\plain \s15\sa60\sl360\slmult0\nowidctlpar\widctlpar\adjustright \f44\cgrid {
\par }}